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A005147
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Denominators of numbers occurring in continued fraction connected with expansion of gamma function.
(Formerly M4831)
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3
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12, 30, 210, 371, 22737, 19733142, 48264275462, 9769214287853155785, 113084128923675014537885725485, 5271244267917980801966553649147604697542, 24274291553105128438297398108902195365373879212227726, 13346384670164266280033479022693768890138348905413621178450736182873
(list;
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listen;
history;
text;
internal format)
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OFFSET
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0,1
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 258.
B. W. Char, On Stieltjes' continued fraction for the gamma function, Math. Comp., 34 (1980), 547-551.
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..30
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 258.
Peter Luschny, Maple program for A005146/A005147
Peter Luschny, Continued fraction
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MATHEMATICA
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len = 12; s[p_] := (-1)^p * BernoulliB[2p+2]/(2p+1)/(2p+2); Do[m[n, 1] = 0, {n, 0, len}]; Do[m[n, 2] = s[n+1]/s[n], {n, 0, len-1}]; Do[m[n, k] =
If[OddQ[k], m[n+1, k-2]+m[n+1, k-1]-m[n, k-1],
m[n+1, k-2]*m[n+1, k-1]/m[n, k-1]], {k, 3, len}, {n, 0,
len-k+1}]; Do[m[n, 1] = s[n], {n, 0, len}];
Table[m[0, k], {k, 1, len}] // Denominator
(* Jean-François Alcover, May 24 2011, after P. Luschny *)
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CROSSREFS
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Cf. A005146.
Sequence in context: A080563 A221520 A214311 * A007308 A065138 A008841
Adjacent sequences: A005144 A005145 A005146 * A005148 A005149 A005150
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KEYWORD
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nonn,frac,nice
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AUTHOR
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Simon Plouffe and N. J. A. Sloane.
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EXTENSIONS
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More terms from Rainer Rosenthal, Jan 11 2007
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STATUS
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approved
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