A192061 Number of 12-core partitions of n.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 65, 89, 111, 140, 171, 213, 253, 310, 363, 432, 498, 583, 705, 800, 924, 1060, 1216, 1379, 1578, 1772, 2013, 2259, 2554, 2847, 3147, 3507, 3897, 4305, 4756, 5225, 5748, 6297, 6909, 7546, 8250, 9000, 9724, 10626, 11512, 12478, 13482, 14616, 15714, 17007, 18215, 19602, 20930, 22470

Offset: 0

Author

N. J. A. Sloane, Jun 21 2011

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz)

Crossrefs

A column of A175595.

Programs

Maple

M:=60;
f:=proc(t) global M; local q,i,t1;
t1:=1;
for i from 1 to M+1 do
t1:=series(t1*(1-q^(i*t))^t,q,M);
t1:=series(t1/(1-q^i),q,M);
od;
t1;
end;
seriestolist(f(12));

Mathematica

m = 60;
f[0] = 1/(1 - x^k);
f[t_] = (1 - x^(k t))^t/(1 - x^k);
s[t_] := CoefficientList[Series[Product[f[t], {k, m-1}], {x, 0, m-1}], x];
s[12] (* Jean-François Alcover, May 27 2020 *)