A379610 a(n) = Sum_{j=0..n} binomial(2*j,j)^4 * binomial(n,j)^2 * Sum_{k=0..n} binomial(k+j,k-j)^2 * binomial(2*j,n-k) * binomial(2*j,k-j).

1, 16, 2576, 1383568, 873960976, 615833930816, 526152430612496, 502263183380000576, 507670642053018634768, 542989589742114444434176, 609997002301177503142835776, 710665335270156912049219940096, 853208134042451055649274133396496, 1051685299255545900736463773134099328

Offset: 0

Author

Seiichi Manyama, Dec 27 2024

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Schmidt's Problem

Crossrefs

Fifth row of array A094424.

Cf. A092815.

Programs

PARI

a(n) = sum(j=0, n, binomial(2*j, j)^4*binomial(n, j)^2*sum(k=0, n, binomial(k+j, k-j)^2*binomial(2*j, n-k)*binomial(2*j, k-j)));

Formula

A092815(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+k,k) * a(k).