cp's OEIS Frontend

A182804 Number of 9-core partitions of n.

%I A182804 #15 May 21 2018 10:44:21
%S A182804 1,1,2,3,5,7,11,15,22,21,33,38,50,56,72,77,96,99,142,139,177,180,228,
%T A182804 229,288,284,357,343,430,410,519,491,615,588,745,714,832,811,1007,939,
%U A182804 1152,1077,1310,1215,1456,1426,1686,1580,1887,1778,2137
%N A182804 Number of 9-core partitions of n.
%H A182804 Alois P. Heinz, <a href="/A182804/b182804.txt">Table of n, a(n) for n = 0..10000</a>
%F A182804 G.f.: Product_{i>=1} (1-x^(9*i))^9/(1-x^i).
%F A182804 Euler transform of period 9 sequence [1,1,1,1,1,1,1,1,-8, .. ].
%p A182804 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);
%t A182804 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 A182804 Table[A[n, 9], {n, 0, 50}] (* _Jean-François Alcover_, May 21 2018, translated from Maple *)
%Y A182804 9th column of A175595.
%K A182804 nonn
%O A182804 0,3
%A A182804 _Alois P. Heinz_, Dec 03 2010