A336979 Expansion of Product_{k>=1} (1 + x^k * (k + x)).

1, 1, 3, 6, 11, 21, 37, 69, 108, 192, 312, 522, 827, 1297, 2032, 3240, 4982, 7569, 11508, 17107, 25696, 38340, 57080, 83298, 121373, 175653, 253455, 364307, 523650, 747487, 1063375, 1498471, 2106317, 2955154, 4124071, 5750547, 8000706, 11104596, 15324290, 21093106

Offset

0,3

Links

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

Formula

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

Mathematica

m = 39; CoefficientList[Series[Product[1 + x^k*(k + x), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, May 01 2021 *)

Prog

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

Crossrefs

Cf. A022629, A160571, A336975, A336976, A336977, A336978, A336980.

Sequence in context: A122106 A007707 A298798 * A018174 A050951 A291408

Adjacent sequences: A336976 A336977 A336978 * A336980 A336981 A336982

Keyword

nonn

Author

Seiichi Manyama, Aug 09 2020

Status

approved