A182803 Number of 8-core partitions of n.

1, 1, 2, 3, 5, 7, 11, 15, 14, 22, 26, 32, 37, 45, 47, 56, 75, 77, 89, 102, 111, 124, 142, 147, 167, 182, 196, 210, 242, 249, 288, 322, 299, 349, 382, 393, 423, 467, 453, 499, 570, 563, 602, 669, 649, 716, 772, 754, 843, 907, 884

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

8th 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,8), 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, 8], {n, 0, 50}] (* Jean-François Alcover, May 21 2018, translated form Maple *)

Formula

G.f.: Product_{i>=1} (1-x^(8*i))^8/(1-x^i).

Euler transform of period 8 sequence [1,1,1,1,1,1,1,-7, .. ].