A382859 a(n) = Sum_{k=0..n} binomial(n,k) * binomial((n-1)*(k+1),n-k).

1, 1, 5, 37, 345, 3851, 49468, 713931, 11391985, 198523495, 3741919446, 75702725440, 1633591960883, 37404262517506, 904734768056239, 23030071358784701, 614912094171482849, 17172036245893988575, 500281954849350450946, 15170753984617328108901

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..150

Formula

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

Mathematica

Table[Sum[Binomial[n, k] * Binomial[(n-1)*(k+1), n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial((n-1)*(k+1), n-k));
(Magma) [&+[Binomial(n, k) * Binomial((n-1)*(k+1), n-k): k in [0..n]]: n in [0..21]]; // Vincenzo Librandi, Apr 09 2025

Crossrefs

Main diagonal of A381425.

Cf. A121673, A121674, A121675.

Sequence in context: A246540 A365842 A177395 * A379994 A370343 A258296

Adjacent sequences: A382856 A382857 A382858 * A382860 A382861 A382862

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 07 2025

Status

approved