A380666 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-x/(1 - x)^2) ).

1, 3, 33, 670, 20193, 812736, 41056921, 2499780144, 178288822305, 14584953692800, 1346528845766481, 138513476506770432, 15711724851356153857, 1948422564510092267520, 262263690685637016402825, 38082186820362623941236736, 5933845220766237850177220289, 987599486681637240983472930816

Offset: 0

Author

Seiichi Manyama, Jan 30 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A380665.

Programs

PARI

a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(3*n+k+1, n-k)/k!);

Formula

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

a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(3*n+k+1,n-k)/k!.