A336980 Expansion of Product_{k>=1} (1 + x^k * (1 + k*x)).

1, 1, 2, 4, 8, 13, 22, 39, 65, 104, 160, 263, 413, 646, 975, 1479, 2198, 3354, 5017, 7389, 10770, 15721, 22668, 32663, 47200, 67761, 96389, 135977, 191431, 268805, 376211, 523692, 730301, 1014029, 1401553, 1925074, 2638522, 3608182, 4924194, 6694070, 9088239, 12323707, 16668255

Offset: 0

Author

Seiichi Manyama, Aug 09 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A160571, A336975, A336976, A336977, A336978, A336979.

Programs

Mathematica

m = 42; CoefficientList[Series[Product[1 + x^k*(1 + k*x), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, Apr 29 2021 *)

PARI

N=66; x='x+O('x^N); Vec(prod(k=1, N, 1+x^k*(1+k*x)))

PARI

N=66; x='x+O('x^N); Vec(exp(sum(k=1, N, x^k*sumdiv(k, d, (-1)^(d+1)*(1+k/d*x)^d/d))))

Formula

G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (-1)^(d+1) * (1 + k/d * x)^d / d).