A137610 Self-convolution of A014062, where A014062(n) = C(n^2, n).

1, 2, 13, 180, 3844, 110908, 4030740, 176640072, 9059743648, 532179428700, 35219852623888, 2592514449263656, 210072673380786552, 18579938909696752728, 1780987027765227959096, 183907984490301947455872

Offset: 0

Author

Paul D. Hanna, Jan 29 2008

Keywords

• nonn

Crossrefs

Cf. A014062.

Programs

Mathematica

Table[Sum[Binomial[k^2, k]*Binomial[(n-k)^2, n-k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Aug 20 2025 *)

PARI

a(n)=sum(k=0,n,binomial(k^2,k)*binomial((n-k)^2,n-k))

Formula

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

a(n) ~ sqrt(2) * exp(n - 1/2) * n^(n - 1/2) / sqrt(Pi). - Vaclav Kotesovec, Aug 20 2025