A374676 a(n) = Sum_{k=0..n} binomial(n+k-1,n) * binomial(n+k,n)^2.

1, 4, 117, 4416, 191025, 8959098, 443175257, 22764880288, 1202693106969, 64935435950760, 3567189106107044, 198746486074429164, 11203798260525398593, 637866038409406067394, 36624374381748740836905, 2118319467225018572438976, 123307986154526506959597225

Offset: 0

Author

Seiichi Manyama, Jul 16 2024

Keywords

• nonn

Crossrefs

Cf. A001791, A374675.

Cf. A112028.

Programs

PARI

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

Formula

a(n) = Sum_{k=0..n} (k/(n+k)) * binomial(n+k,k)^3 for n > 0.