A372087 G.f. A(x) satisfies A(x) = 1/( 1 - 9*x*(1 + x)*A(x) )^(1/3).

1, 3, 30, 369, 5130, 76626, 1200816, 19475829, 324140886, 5504511654, 94998663000, 1661370690546, 29377608173460, 524366947411668, 9435112261205328, 170958245619049173, 3116653690408787070, 57125853834377116014, 1052116816793294021688

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = Sum_{k=0..n} 9^k * binomial(4*k/3-2/3,k) * binomial(k,n-k)/(k+1).

Prog

(PARI) a(n) = sum(k=0, n, 9^k*binomial(4*k/3-2/3, k)*binomial(k, n-k)/(k+1));

Crossrefs

Cf. A180400, A372038.

Sequence in context: A365158 A178016 A365152 * A357770 A372105 A372091

Adjacent sequences: A372084 A372085 A372086 * A372088 A372089 A372090

Keyword

nonn

Author

Seiichi Manyama, Apr 17 2024

Status

approved