A379456 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + x*exp(x)) ).

1, 2, 13, 151, 2573, 58221, 1648345, 56138461, 2236816825, 102135829609, 5259937376141, 301678137203433, 19072415186892325, 1317869007328182349, 98818139178323981473, 7991908824553634264101, 693473520767940388417265, 64266613784795934251538513

Offset

0,2

Links

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

Formula

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

E.g.f. A(x) satisfies A(x) = exp(x*A(x)) / ( 1 - x*exp(2*x*A(x)) ). - Seiichi Manyama, Feb 04 2025

Prog

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

Crossrefs

Cf. A088690, A379846, A379847.

Cf. A108919, A161633.

Cf. A379699, A379700.

Sequence in context: A363846 A058192 A380717 * A367820 A377831 A054382

Adjacent sequences: A379453 A379454 A379455 * A379457 A379458 A379459

Keyword

nonn

Author

Seiichi Manyama, Dec 30 2024

Status

approved