A341225 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^6.

1, 12, 78, 370, 1437, 4848, 14719, 41148, 107610, 266296, 628941, 1427118, 3127369, 6646440, 13746081, 27744926, 54782271, 106029918, 201512970, 376630680, 693161334, 1257641676, 2251764699, 3982196910, 6961522279, 12038699766, 20607718317, 34938910360

Offset: 6

Author

Ilya Gutkovskiy, Feb 07 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..10000

Crossrefs

Column k=6 of A060642.

Cf. A000041, A023005, A048574, A327384, A341221, A341222, A341223, A341226, A341227, A341228.

Programs

Maple

b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, combinat[
      numbpart](n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
    end:
a:= n-> b(n, 6):
seq(a(n), n=6..33);  # Alois P. Heinz, Feb 07 2021

Mathematica

nmax = 33; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^6, {x, 0, nmax}], x] // Drop[#, 6] &