A391382 Expansion of g*(1 + x*g^3), where g = 1+x*g^5 is the g.f. of A002294.

1, 2, 9, 61, 489, 4301, 40131, 390104, 3907977, 40062412, 418254034, 4431613550, 47532700995, 515094994701, 5631040056392, 62026042961616, 687736507905865, 7669858226447790, 85977241224449355, 968212072361926899, 10948257397698469394, 124260575713288452130

Offset

0,2

Links

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

Formula

G.f.: 2 - 1/B(x), where B(x) is the g.f. of A391383.

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

a(n) = binomial(5*n+1,n)/(5*n+1) + binomial(5*n-1,n)/(5*n-1) for n > 0.

Prog

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

Crossrefs

Cf. A167422, A391380, A391381.

Cf. A002294.

Sequence in context: A207649 A289713 A341956 * A349289 A053983 A370161

Adjacent sequences: A391379 A391380 A391381 * A391383 A391384 A391385

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 08 2025

Status

approved