A192061 - OEIS

%I #20 May 27 2020 09:55:22

%S 1,1,2,3,5,7,11,15,22,30,42,56,65,89,111,140,171,213,253,310,363,432,

%T 498,583,705,800,924,1060,1216,1379,1578,1772,2013,2259,2554,2847,

%U 3147,3507,3897,4305,4756,5225,5748,6297,6909,7546,8250,9000,9724,10626,11512,12478,13482,14616,15714,17007,18215,19602,20930,22470

%N Number of 12-core partitions of n.

%H Seiichi Manyama, <a href="/A192061/b192061.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Alois P. Heinz)

%p M:=60;

%p f:=proc(t) global M; local q,i,t1;

%p t1:=1;

%p for i from 1 to M+1 do

%p t1:=series(t1*(1-q^(i*t))^t,q,M);

%p t1:=series(t1/(1-q^i),q,M);

%p od;

%p t1;

%p end;

%p seriestolist(f(12));

%t m = 60;

%t f[0] = 1/(1 - x^k);

%t f[t_] = (1 - x^(k t))^t/(1 - x^k);

%t s[t_] := CoefficientList[Series[Product[f[t], {k, m-1}], {x, 0, m-1}], x];

%t s[12] (* _Jean-François Alcover_, May 27 2020 *)

%Y A column of A175595.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jun 21 2011