A379699 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + 2*x*exp(x)) ).

1, 3, 27, 430, 10013, 309146, 11932303, 553740958, 30053978361, 1868855561938, 131048808861491, 10232894227577462, 880688476587319573, 82836081054992159194, 8454536286883278469431, 930656450818831650930766, 109910217042754940709650417, 13862746369348872200671305890

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) * (2*n-k+1)^k * binomial(n+1,n-k)/k!.

Prog

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

Crossrefs

Cf. A201470, A377373.

Cf. A379456, A379700.

Sequence in context: A094577 A221624 A108525 * A136719 A377361 A279844

Adjacent sequences: A379694 A379697 A379698 * A379700 A379701 A379702

Keyword

nonn,new

Author

Seiichi Manyama, Dec 30 2024

Status

approved