A362084 a(n) = Sum_{k=0..n} (-1)^k * binomial(-2,k) * binomial(n*k,n-k).

1, 2, 7, 28, 145, 896, 6328, 50212, 441489, 4248370, 44306306, 496991848, 5959111223, 75977511442, 1025441134747, 14594189335496, 218290221112929, 3421314388169988, 56043004143343843, 957209642080023286, 17011439135301438016, 313980693855333453740

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..493

Formula

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

a(n) = [x^n] 1/(1 - x*(1+x)^n)^2.

Prog

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

Crossrefs

Column k=2 of A362079.

Cf. A099237.

Sequence in context: A030946 A030906 A307594 * A296726 A334613 A365559

Adjacent sequences: A362081 A362082 A362083 * A362085 A362086 A362087

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2023

Status

approved