A336990 Expansion of Product_{k>=1} 1/(1 - x^k / (1 - k*x)).

1, 1, 3, 8, 22, 62, 182, 560, 1822, 6316, 23467, 93762, 402989, 1858904, 9165303, 48065800, 266791060, 1560140592, 9573440644, 61431041813, 411006873603, 2859978776644, 20653331408062, 154494203986783, 1195107012223439, 9546189429869925, 78632580076861376, 667111706008969377

Offset: 0

Author

Seiichi Manyama, Aug 10 2020

Keywords

• nonn

Crossrefs

Cf. A227682, A336989, A336991.

Programs

Mathematica

m = 27; CoefficientList[Series[Product[1/(1 - x^k/(1 - k*x)), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, Aug 10 2020 *)

PARI

N=40; x='x+O('x^N); Vec(1/prod(k=1, N, 1-x^k/(1-k*x)))

PARI

N=40; x='x+O('x^N); Vec(exp(sum(k=1, N, x^k*sumdiv(k, d, 1/(d*(1-k/d*x)^d)))))

Formula

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