A391380 Expansion of g*(1 + x*g), where g = 1+x*g^3 is the g.f. of A001764.

1, 2, 5, 19, 85, 416, 2156, 11628, 64581, 366850, 2121405, 12446655, 73908588, 443329264, 2682282440, 16350019688, 100312427493, 618978133158, 3838830395855, 23916064782225, 149605584539565, 939295627587240, 5917060156672560, 37387903504202160

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

G.f.: 2 - 1/B(x), where B(x) is the g.f. of A390519.

G.f.: 1 + g - 1/g, where g = 1+x*g^4 is the g.f. of A001764.

a(n) = binomial(3*n+1,n)/(3*n+1) + binomial(3*n-1,n)/(3*n-1) for n > 0.

Prog

(PARI) a(n) = if(n==0, 1, binomial(3*n+1, n)/(3*n+1)+binomial(3*n-1, n)/(3*n-1));

Crossrefs

Cf. A167422, A391381, A391382.

Cf. A001764, A101409, A390519.

Sequence in context: A107377 A286886 A058132 * A286071 A002851 A354621

Adjacent sequences: A391377 A391378 A391379 * A391381 A391382 A391383

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 08 2025

Status

approved