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

0,2

Links

Table of n, a(n) for n=0..21.

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).

Prog

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

Crossrefs

Cf. A025227, A381787, A381937.

Cf. A002293, A346647, A365184.

Sequence in context: A362340 A324513 A086902 * A265042 A249754 A224879

Adjacent sequences: A381937 A381938 A381939 * A381941 A381942 A381943

Keyword

nonn,new

Author

Seiichi Manyama, Mar 10 2025

Status

approved