A341236 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^10.

1, 20, 210, 1550, 9055, 44624, 192945, 751480, 2686155, 8934560, 27946335, 82884860, 234636435, 637416140, 1669127130, 4228739712, 10398140075, 24882425770, 58080468790, 132508486900, 296005537183, 648445364080, 1394961003490, 2950516502980, 6142674032345, 12599932782780

Offset: 10

Author

Ilya Gutkovskiy, Feb 07 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..10000

Crossrefs

Column k=10 of A060642.

Cf. A000041, A023009, A048574, A327388, A341221, A341222, A341223, A341225, 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, 10):
seq(a(n), n=10..35);  # Alois P. Heinz, Feb 07 2021

Mathematica

nmax = 35; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^10, {x, 0, nmax}], x] // Drop[#, 10] &