A355428 a(n) = n! * [x^n] 1/(1 - Sum_{k=1..n} (exp(k*x) - 1)/k).

1, 1, 11, 284, 13564, 1037479, 116171621, 17916010524, 3640962169776, 942959405612913, 303168464105203113, 118474395231479349050, 55306932183983923942940, 30397993745996492901617435, 19429788681469866219869997285

Offset: 0

Author

Seiichi Manyama, Jul 01 2022

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..226

Crossrefs

Main diagonal of A355427.

Cf. A319508.

Programs

Mathematica

Table[n! * SeriesCoefficient[1/(1 + HarmonicNumber[n] + E^((n + 1)*x) * LerchPhi[E^x, 1, n + 1] + Log[1 - E^x]), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 02 2022 *)

PARI

a(n) = n!*polcoef(1/(1-sum(k=1, n, (exp(k*x+x*O(x^n))-1)/k)), n);

Formula

a(n) ~ c * d^n * n^(2*n + 1/2), where d = 0.4573611067742364103005235654624761643997061199669064548746966610712579358... and c = 2.41592773370058066984975000807924527905758896927935098069320182397... - Vaclav Kotesovec, Jul 02 2022