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

0,3

Links

Table of n, a(n) for n=0..22.

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.

Mathematica

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

Prog

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

Crossrefs

Column k=2 of A362078.

Cf. A362084.

Sequence in context: A274674 A255672 A077239 * A046235 A297329 A347726

Adjacent sequences: A362084 A362085 A362086 * A362088 A362089 A362090

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2023

Status

approved