A038744 a(n) = T(2n,n), array T as in A038738.

1, 5, 30, 188, 1201, 7756, 50439, 329625, 2161974, 14220038, 93740152, 619083041, 4094863900, 27120465023, 179822255181, 1193481705940, 7927993075073, 52704055853440, 350609068027203, 2333840093532306, 15543999383823744, 103580158099915047, 690547856312462805

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

G.f.: (g-1)/((3*g-1)*(g^2-3*g+1)) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011

From Seiichi Manyama, Oct 30 2025: (Start)

a(n) = Sum_{k=0..n} binomial(3*n+k+1,n-k).

G.f.: g/((1-3*x*g^2) * (1-x*g^4)) where g = 1+x*g^3 is the g.f. of A001764. (End)

a(n) = Sum_{k=0..n} binomial(3*n+1,n-k) * Fibonacci(k+1). - Seiichi Manyama, Nov 01 2025

a(n) ~ 3^(3*n + 3/2) / (sqrt(Pi*n) * 4^n). - Vaclav Kotesovec, Nov 09 2025

Crossrefs

Cf. A025174, A160906, A263134.

Cf. A038736, A390238.

Cf. A000045, A001764, A038738, A038792.

Sequence in context: A006773 A059273 A352175 * A098663 A265085 A158828

Adjacent sequences: A038741 A038742 A038743 * A038745 A038746 A038747

Keyword

nonn

Author

Clark Kimberling, May 02 2000

Extensions

More terms from Seiichi Manyama, Oct 30 2025

Status

approved