A374675 a(n) = Sum_{k=0..n} binomial(n+k-1,n) * binomial(n+k,n).

1, 2, 21, 244, 3055, 40116, 544103, 7553960, 106734195, 1528937200, 22143771386, 323613807672, 4765050473521, 70611124679564, 1052084386116915, 15750153504353872, 236766112174722235, 3572264808332407512, 54073065371555283968, 820886646834780680640

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} (k/(n+k)) * binomial(n+k,k)^2 for n > 0.

a(n) = (n+1) * A259335(n).

Prog

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

Crossrefs

Cf. A001791, A374676.

Cf. A112029, A129763, A259335.

Sequence in context: A045726 A105712 A087677 * A266969 A229036 A097627

Adjacent sequences: A374672 A374673 A374674 * A374676 A374677 A374678

Keyword

nonn

Author

Seiichi Manyama, Jul 16 2024

Status

approved