A380801 Expansion of e.g.f. ( (1/x) * Series_Reversion( x * exp(-x / (1 - x)^2) ) )^2.

1, 2, 16, 206, 3792, 91402, 2733376, 97793334, 4078001920, 194355934802, 10426538225664, 621994665546718, 40852668904155136, 2929900797265945050, 227853412116442243072, 19100256246157081925318, 1716982264495843606462464, 164771462679434867316243874

Offset: 0

Author

Seiichi Manyama, Feb 04 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A364939.

Programs

PARI

a(n, q=2, r=1, s=1, t=2, u=0) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364939.

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

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