A341228 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^9.

1, 18, 171, 1149, 6147, 27891, 111567, 403722, 1345896, 4189334, 12300174, 34337403, 91721385, 235645425, 584759880, 1406588073, 3289489002, 7498465029, 16697615817, 36391839264, 77758115283, 163123713621, 336420277812, 682877289213, 1365674365197, 2693384989056

Offset: 9

Author

Ilya Gutkovskiy, Feb 07 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..10000

Crossrefs

Column k=9 of A060642.

Cf. A000041, A023008, A048574, A327387, A341221, A341222, A341223, A341225, A341226, A341227.

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, 9):
seq(a(n), n=9..34);  # Alois P. Heinz, Feb 07 2021

Mathematica

nmax = 34; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^9, {x, 0, nmax}], x] // Drop[#, 9] &