A377789 - OEIS

A377789

Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - 2*log(1-x)) ).

1, 2, 10, 88, 1148, 20088, 442896, 11802096, 369132256, 13261156416, 538227938880, 24359100451200, 1216403663398656, 66440221207025664, 3940468338389603328, 252190997066643909120, 17324237625466992906240, 1271459220768570290626560, 99289436336361780797288448

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

Index entries for reversions of series

FORMULA

a(n) = n! * Sum_{k=0..n} 2^k * |Stirling1(n,k)|/(n-k+1)!.

E.g.f. A(x) satisfies: A(x) = 1 - 2*log(1 - x*A(x)). - Ilya Gutkovskiy, Jun 10 2026

PROG

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1-2*log(1-x)))/x))

(PARI) a(n) = n!*sum(k=0, n, 2^k*abs(stirling(n, k, 1))/(n-k+1)!);