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

0,2

Links

Table of n, a(n) for n=0..16.

Formula

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

Prog

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

Crossrefs

Cf. A001791, A374675.

Cf. A112028.

Sequence in context: A194535 A030255 A146508 * A365450 A096464 A285053

Adjacent sequences: A374673 A374674 A374675 * A374677 A374678 A374679

Keyword

nonn

Author

Seiichi Manyama, Jul 16 2024

Status

approved