A341221 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^3.

1, 6, 21, 59, 144, 321, 669, 1323, 2511, 4604, 8202, 14253, 24241, 40449, 66363, 107234, 170910, 269004, 418566, 644436, 982536, 1484482, 2223942, 3305484, 4876620, 7144455, 10398123, 15039564, 21624678, 30919323, 43973708, 62222844, 87619212, 122810585

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..10000

Formula

a(n) ~ A000716(n). - Vaclav Kotesovec, Feb 20 2021

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, 3):
seq(a(n), n=3..36);  # Alois P. Heinz, Feb 07 2021

Mathematica

nmax = 36; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^3, {x, 0, nmax}], x] // Drop[#, 3] &

Crossrefs

Column k=3 of A060642.

Cf. A000041, A000716, A048574, A327381, A341222, A341223, A341225, A341226, A341227, A341228.

Sequence in context: A290891 A047520 A294836 * A143115 A258142 A321257

Adjacent sequences: A341218 A341219 A341220 * A341222 A341223 A341224

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 07 2021

Status

approved