A362087 a(n) = Sum_{k=0..n} (-1)^k * binomial(-n,k) * binomial(2*k,n-k).

1, 1, 7, 37, 215, 1271, 7651, 46614, 286599, 1774630, 11050897, 69134572, 434174819, 2735565574, 17283825370, 109466361512, 694764983463, 4417771590123, 28137563496298, 179478199605550, 1146342590242465, 7330598365285470, 46928753892901140

Offset: 0

Author

Seiichi Manyama, Apr 08 2023

Keywords

• nonn

Crossrefs

Column k=2 of A362078.

Cf. A362084.

Programs

Mathematica

Table[Sum[Binomial[n + k - 1, k]*Binomial[2*k, n-k], {k, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Apr 08 2023 *)

PARI

a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(2*k, n-k));

Formula

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

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