A379700 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + 3*x*exp(x)) ).

1, 4, 45, 889, 25613, 977271, 46586281, 2669066695, 178800270009, 13720918482235, 1187217400278941, 114379273346497611, 12144899525595998821, 1409261040317551952935, 177436990866294436727409, 24094164269339964351367231, 3510079015962779901366174449, 546103202348225740056486964467

Offset

0,2

Links

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

Formula

a(n) = (n!/(n+1)) * Sum_{k=0..n} 3^(n-k) * (2*n-k+1)^k * binomial(n+1,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, 3^(n-k)*(2*n-k+1)^k*binomial(n+1, n-k)/k!)/(n+1);

Crossrefs

Cf. A379456, A379699.

Cf. A377374.

Sequence in context: A360344 A197989 A377830 * A338456 A276292 A174484

Adjacent sequences: A379697 A379698 A379699 * A379701 A379702 A379703

Keyword

nonn

Author

Seiichi Manyama, Dec 30 2024

Status

approved