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A182804
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Number of 9-core partitions of n.
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3
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1, 1, 2, 3, 5, 7, 11, 15, 22, 21, 33, 38, 50, 56, 72, 77, 96, 99, 142, 139, 177, 180, 228, 229, 288, 284, 357, 343, 430, 410, 519, 491, 615, 588, 745, 714, 832, 811, 1007, 939, 1152, 1077, 1310, 1215, 1456, 1426, 1686, 1580, 1887, 1778, 2137
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..10000
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FORMULA
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G.f.: Product_{i>=1} (1-x^(9*i))^9/(1-x^i).
Euler transform of period 9 sequence [1,1,1,1,1,1,1,1,-8, .. ].
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MAPLE
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with(numtheory): A:= proc(n, t) option remember; local d, j; `if`(n=0, 1, add(add(`if`(t=0 or irem(d, t)=0, d-d*t, d), d=divisors(j)) *A(n-j, t), j=1..n)/n) end: seq(A(n, 9), n=0..50);
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MATHEMATICA
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A[n_, t_] := A[n, t] = If[n == 0, 1, Sum[Sum[If[t == 0 || Mod[d, t] == 0, d - d*t, d], {d, Divisors[j]}]*A[n - j, t], {j, 1, n}]/n] ;
Table[A[n, 9], {n, 0, 50}] (* Jean-François Alcover, May 21 2018, translated from Maple *)
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CROSSREFS
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9th column of A175595.
Sequence in context: A027342 A184643 A307547 * A242695 A319473 A085894
Adjacent sequences: A182801 A182802 A182803 * A182805 A182806 A182807
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Dec 03 2010
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STATUS
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approved
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