A330150 Expansion of e.g.f. exp(-x) / (1 - log(1 + x)).

1, 0, 0, 1, -1, 8, -16, 159, -659, 6824, -46680, 517581, -4941685, 61043344, -735256328, 10269016939, -147207286503, 2322683458544, -38298239486672, 677630804946393, -12581447014620585, 247342217288517496, -5096876494438056928, 110338442309322274295

Offset: 0

Author

Ilya Gutkovskiy, Dec 03 2019

Keywords

• sign

Comments

Inverse binomial transform of A006252.

Crossrefs

Cf. A052841, A330149.

Cf. A006252, A291981.

Programs

Mathematica

nmax = 23; CoefficientList[Series[Exp[-x]/(1 - Log[1 + x]), {x, 0, nmax}], x] Range[0, nmax]!

Formula

a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * A006252(k).

a(n) = (-1)^n + Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Dec 19 2023