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A002622
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Number of partitions of at most n into at most 5 parts.
(Formerly M1053 N0395)
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4
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1, 2, 4, 7, 12, 19, 29, 42, 60, 83, 113, 150, 197, 254, 324, 408, 509, 628, 769, 933, 1125, 1346, 1601, 1892, 2225, 2602, 3029, 3509, 4049, 4652, 5326, 6074, 6905, 7823, 8837, 9952, 11178, 12520, 13989, 15591, 17338, 19236, 21298, 23531, 25949, 28560, 31378, 34412
(list;
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listen;
history;
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internal format)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
E. Fix and J. L. Hodges, Jr., Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312.
E. Fix and J. L. Hodges, Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312. [Annotated scanned copy]
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FORMULA
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G.f.: 1/[(1+x^2)(1-x^3)(1-x)^4(1-x^5)].
G.f.: 1 / ((1 - x)^2 * (1 - x^2) * (1 - x^3) * (1 - x^4) * (1 - x^5)). - Michael Somos, Apr 24 2014
Euler transform of length 5 sequence [ 2, 1, 1, 1, 1]. - Michael Somos, Apr 24 2014
a(n) = a(n-1) + A001401(n). - Michael Somos, Apr 24 2014
a(n) = round((n+1)*(6*n^4+234*n^3+3326*n^2+20674*n+50651+675*(-1)^n)/86400). - Tani Akinari, May 05 2014
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EXAMPLE
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G.f. = 1 + 2*x + 4*x^2 + 7*x^3 + 12*x^4 + 19*x^5 + 29*x^6 + 42*x^7 + 60*x^8 + ...
a(2) = 4 with partitions 0, 1, 2, 1+1. a(3) = 7 with partitions 0, 1, 2, 1+1, 3, 2+1, 1+1+1. - Michael Somos, Apr 24 2014
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MATHEMATICA
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CoefficientList[Series[1/((1 - x)^2 (1 - x^2) (1 - x^3) (1 - x^4) (1 - x^5)), {x, 0, 100}], x] (* Vincenzo Librandi, Apr 25 2014 *)
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CROSSREFS
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Cf. A001401.
Sequence in context: A087149 A090853 A103231 * A035301 A035297 A153252
Adjacent sequences: A002619 A002620 A002621 * A002623 A002624 A002625
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Vincenzo Librandi, Apr 25 2014
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STATUS
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approved
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