A377392 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*(exp(x) - 1))^2 ).

1, 0, 4, 6, 224, 1330, 42912, 548114, 18337440, 382829346, 14098368080, 413342914402, 17124811116624, 644015140354898, 30163665817167456, 1375047846420311730, 72583022771706823232, 3866142693873431519554, 228486372085027819754928, 13871056133441358772777154

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Index entries for reversions of series

Formula

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371270.

a(n) = 2 * n! * (2*n+1)! * Sum_{k=0..floor(n/2)} Stirling2(n-k,k)/( (n-k)! * (2*n-k+2)! ).

Prog

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

Crossrefs

Cf. A371119, A377393.

Cf. A371270.

Sequence in context: A298147 A081970 A076098 * A377390 A141568 A376381

Adjacent sequences: A377389 A377390 A377391 * A377393 A377394 A377395

Keyword

nonn

Author

Seiichi Manyama, Oct 27 2024

Status

approved