A380828 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-2*x) / (1 + x) ).

1, 3, 26, 398, 8904, 264072, 9790192, 436382256, 22748241024, 1358633214080, 91503397265664, 6862436244211968, 567252637423922176, 51244493078278198272, 5023312927780022323200, 531082672018567209801728, 60239691905397303186849792, 7297357396264290237329473536

Offset: 0

Author

Seiichi Manyama, Feb 05 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A352448, A380808.

Cf. A088690, A380830.

Cf. A376093.

Programs

PARI

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

Formula

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

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

a(n) = A376093(n+1)/(n+1).