A364331 G.f. satisfies A(x) = (1 + x*A(x)^2) * (1 + x*A(x)^5).

1, 2, 15, 163, 2070, 28698, 421015, 6425644, 100977137, 1622885389, 26551709946, 440744175801, 7404449354076, 125657625548824, 2150963575012295, 37094953102567208, 643904274979347286, 11241232087809137759, 197247501440314516840, 3476787208220672891388, 61533794803235280779261

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..n} binomial(2*n+3*k+1,k) * binomial(2*n+3*k+1,n-k) / (2*n+3*k+1).

x/(series_reversion(x*A(x)) = 1 + 2*x + 11*x^2 + 89*x^3 + 836*x^4 + ..., the g.f. of A215623. - Peter Bala, Sep 08 2024

Maple

A364331 := proc(n)
    add( binomial(2*n+3*k+1, k) * binomial(2*n+3*k+1, n-k)/(2*n+3*k+1), k=0..n) ;
end proc:
seq(A364331(n), n=0..70); # R. J. Mathar, Jul 25 2023

Prog

(PARI) a(n) = sum(k=0, n, binomial(2*n+3*k+1, k)*binomial(2*n+3*k+1, n-k)/(2*n+3*k+1));

Crossrefs

Cf. A007863, A069271, A073157, A215654, A215715, A364333.

Cf. A215623, A215624, A239108, A364335, A364338.

Cf. A200719.

Sequence in context: A268070 A204679 A363564 * A259608 A317278 A140809

Adjacent sequences: A364328 A364329 A364330 * A364332 A364333 A364334

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 18 2023

Status

approved