A182804 Number of 9-core partitions of n.

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

Offset: 0

Author

Alois P. Heinz, Dec 03 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

9th column of A175595.

Programs

Maple

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);

Mathematica

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 *)

Formula

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, .. ].