%I #16 May 21 2018 10:44:28

%S 1,1,2,3,5,7,11,15,14,22,26,32,37,45,47,56,75,77,89,102,111,124,142,

%T 147,167,182,196,210,242,249,288,322,299,349,382,393,423,467,453,499,

%U 570,563,602,669,649,716,772,754,843,907,884

%N Number of 8-core partitions of n.

%H Alois P. Heinz, <a href="/A182803/b182803.txt">Table of n, a(n) for n = 0..10000</a>

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

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

%p 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);

%t 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];

%t Table[A[n, 8], {n, 0, 50}] (* _Jean-François Alcover_, May 21 2018, translated form Maple *)

%Y 8th column of A175595.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Dec 03 2010