A265953 E.g.f.: Product_{k>=1} 1/(1 - exp(x)*x^k).

1, 1, 6, 39, 328, 3305, 39396, 536053, 8210784, 139670721, 2612934820, 53260680341, 1175587507392, 27929705129521, 710678763809028, 19284199100275845, 555961318128936256, 16972543570002866945, 547046699544108738756, 18566047855851466092949

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..408

Formula

a(n) ~ c * n! / LambertW(1)^n, where c = 1/(1 + LambertW(1)) * Product_{j>=1} 1/(1 - LambertW(1)^j) = 3.40413121452412914124892504613759007312040569..., LambertW(1) = A030178.

Mathematica

nmax=20; CoefficientList[Series[Product[1/(1-E^x*x^k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!

Crossrefs

Cf. A030178, A030797, A265952.

Sequence in context: A341728 A058191 A113347 * A356335 A246571 A031972

Adjacent sequences: A265950 A265951 A265952 * A265954 A265955 A265956

Keyword

nonn

Author

Vaclav Kotesovec, Dec 19 2015

Status

approved