A379862 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x)/(1 + x*exp(x))^2 ).

1, 3, 29, 502, 12761, 430986, 18217813, 926514058, 55133781809, 3760088111938, 289240874117981, 24780044801646762, 2340229465310736073, 241563626661550193794, 27059024800372108029221, 3269263894468329061597546, 423798837014001794141132897, 58674726188995774863597090690

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Index entries for reversions of series

Formula

E.g.f. A(x) satisfies A(x) = exp(x*A(x)) * (1 + x * A(x) * exp(x*A(x)))^2.

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

Mathematica

Table[n! / (n+1) * Sum[(n+k+1)^(n-k) * Binomial[2*n+2, k]/(n-k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 02 2026 *)

Prog

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

Crossrefs

Cf. A377553, A379861.

Cf. A379456.

Sequence in context: A376038 A326433 A113871 * A392566 A377832 A380721

Adjacent sequences: A379859 A379860 A379861 * A379863 A379864 A379865

Keyword

nonn

Author

Seiichi Manyama, Jan 04 2025

Status

approved