A368489 a(n) = Sum_{k=0..n} n^k * binomial(k+n,k).

1, 3, 31, 643, 20421, 873806, 46994011, 3042431715, 230249448841, 19940350062394, 1944516598602711, 210829412453667998, 25156743053019602701, 3275876521195372322892, 462262670054775645538099, 70264375447526610838701091

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

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

a(n) ~ 4^n * n^(n - 1/2) / sqrt(Pi). - Vaclav Kotesovec, Dec 27 2023

Prog

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

Crossrefs

Cf. A001700, A026641, A368488.

Sequence in context: A222895 A373754 A105293 * A104841 A092552 A322487

Adjacent sequences: A368486 A368487 A368488 * A368490 A368491 A368492

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 27 2023

Status

approved