A088815 Expansion of e.g.f. (1-x)^(-1/(1+log(1-x))).

1, 1, 4, 24, 190, 1860, 21638, 291158, 4443556, 75779580, 1427272032, 29409572808, 657829667328, 15868725580344, 410543007882408, 11336582934052104, 332736828827893968, 10342443317857993680, 339343476195341474688

Offset: 0

Author

Vladeta Jovovic, Nov 22 2003

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..410

Crossrefs

Row sums of A079640.

Cf. A000262, A007840, A088819.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[(1-x)^(-1/(1+Log[1-x])), {x,0,nn}], x]Range[0,nn]!] (* Harvey P. Dale, Nov 29 2011 *)

PARI

x='x+O('x^25); Vec(serlaplace((1-x)^(-1/(1+log(1-x))))) \\ G. C. Greubel, Feb 16 2017

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, sum(k=0, j, k!*abs(stirling(j, k, 1)))*binomial(i-1, j-1)*v[i-j+1])); v; \\ Seiichi Manyama, May 23 2022

Formula

a(n) = Sum_{k=0..n} |Stirling1(n, k)|*A000262(k). - Vladeta Jovovic, Nov 26 2003

a(n) ~ n! * exp(n + 2*sqrt(n)/sqrt(exp(1)-1) + 1/(2*(exp(1)-1)) - 1/2) / (2*sqrt(Pi) * (exp(1)-1)^(n+1/4) * n^(3/4)). - Vaclav Kotesovec, May 04 2015

a(0) = 1; a(n) = Sum_{k=1..n} A007840(k) * binomial(n-1,k-1) * a(n-k). - Seiichi Manyama, May 23 2022