A383379 a(n) = n! * Sum_{k=0..n} (-n)^(n-k) * binomial(n+k,n)/(n-k)!.

1, 1, 4, 21, 176, 1765, 22464, 331177, 5692672, 110286441, 2394828800, 57389046781, 1507401363456, 43018690418509, 1326170009092096, 43905977120300625, 1553942522589937664, 58544111242378404433, 2339326913228257886208, 98816004834223734304741

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = n! * [x^n] exp(-n*x) / (1-x)^(n+1).

a(n) ~ phi^(3*n + 3/2) * n^n / (5^(1/4) * exp(phi*n)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Apr 25 2025

Prog

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

Crossrefs

Main diagonal of A383341.

Cf. A295182.

Sequence in context: A317104 A163948 A393740 * A278993 A306067 A230682

Adjacent sequences: A383376 A383377 A383378 * A383380 A383381 A383382

Keyword

nonn

Author

Seiichi Manyama, Apr 24 2025

Status

approved