A391383 Expansion of g/(1 - x*g^6), where g = 1+x*g^5 is the g.f. of A002294.

1, 2, 13, 105, 938, 8893, 87723, 890325, 9232805, 97376126, 1041089019, 11256502919, 122861952973, 1351837036390, 14977717978726, 166953700523302, 1870943152825162, 21065820665414499, 238193982444276850, 2703539335002781050, 30791152935141127601, 351782582241082177731

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} (6*k+1) * binomial(5*n+k+1,n-k)/(5*n+k+1).

G.f.: 1/(1 + 1/g - g), where g = 1+x*g^5 is the g.f. of A002294.

Prog

(PARI) a(n) = sum(k=0, n, (6*k+1)*binomial(5*n+k+1, n-k)/(5*n+k+1));

Crossrefs

Cf. A026726, A390519, A390710.

Cf. A002294, A391382.

Sequence in context: A371583 A083062 A204261 * A371586 A371574 A127746

Adjacent sequences: A391380 A391381 A391382 * A391384 A391385 A391386

Keyword

nonn

Author

Seiichi Manyama, Dec 08 2025

Status

approved