A088819 Expansion of e.g.f. (1+x)^(1/(1-log(1+x))).

1, 1, 2, 6, 22, 100, 518, 3122, 20676, 154524, 1238952, 11030448, 103376832, 1068000024, 11407673496, 134352996744, 1603035004368, 21276244952784, 278535036773856, 4141886572833888, 58405909554175776, 973789956270781056, 14462380128843907680

Offset

0,3

Comments

a(34) is the first negative term.

Links

Georg Fischer, Table of n, a(n) for n = 0..100

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} A006252(k) * binomial(n-1,k-1) * a(n-k). - Seiichi Manyama, May 23 2022

Mathematica

CoefficientList[Series[(1+x)^(1/(1-Log[1+x])), {x, 0, 100}], x]* Range[0, 100]! (* Georg Fischer, Feb 17 2019 *)

Prog

(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!*stirling(j, k, 1))*binomial(i-1, j-1)*v[i-j+1])); v; \\ Seiichi Manyama, May 23 2022

Crossrefs

Row sums of A079639.

Cf. A000262, A006252.

Sequence in context: A012271 A012266 A009468 * A177478 A052517 A245119

Adjacent sequences: A088816 A088817 A088818 * A088820 A088821 A088822

Keyword

sign

Author

Vladeta Jovovic, Nov 22 2003

Status

approved