A330498 Expansion of e.g.f. Sum_{k>=1} log(1 + log(1/(1 - x))^k) / k.

0, 1, 1, 6, 24, 152, 1230, 12646, 141274, 1730984, 23920800, 379364664, 6766026168, 131337466608, 2713274041296, 59397879195456, 1386647548658496, 34745321580075648, 934708252265232768, 26835517455387452928, 815158892950448937984

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Vaclav Kotesovec, Graph - the asymptotic ratio

Formula

a(n) ~ n! * c / (n * (1 - exp(-1))^n), where c = 0.6931..., conjecture: c = log(2).

Mathematica

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

Crossrefs

Cf. A003713, A330352, A330493, A330499.

Sequence in context: A366757 A250743 A265883 * A165491 A165638 A122829

Adjacent sequences: A330495 A330496 A330497 * A330499 A330500 A330501

Keyword

nonn

Author

Vaclav Kotesovec, Dec 16 2019

Status

approved