A381940 G.f. A(x) satisfies A(x) = (1 + x) * B(x*A(x)), where B(x) is the g.f. of A002293.

1, 2, 7, 51, 440, 4170, 41921, 438972, 4736281, 52286520, 587774685, 6705201456, 77426676892, 903251324476, 10629495065550, 126032922655030, 1504194199010435, 18056321542477095, 217859030049153565, 2640609137351540510, 32137554969392230950, 392580762083089376630

Offset: 0

Author

Seiichi Manyama, Mar 10 2025

Keywords

• nonn

Crossrefs

Cf. A025227, A381787, A381937.

Cf. A002293, A346647, A365184.

Programs

PARI

a(n) = sum(k=0, n, binomial(5*k+1, k)*binomial(k+1, n-k)/(5*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(5*k+1,k) * binomial(k+1,n-k)/(5*k+1).

a(n) = A365184(n) + A365184(n-1).