A381819 Expansion of ( (1/x) * Series_Reversion( x * ((1-x) / C(x))^3 ) )^(1/3), where C(x) is the g.f. of A000108.

1, 2, 16, 177, 2271, 31731, 468614, 7195295, 113712012, 1837457589, 30220139048, 504212998955, 8513461623355, 145197727340337, 2497695979786842, 43285207907364178, 755005614380697735, 13244500528948104210, 233515959911770430972, 4135792046643993604967

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

G.f. A(x) satisfies A(x) = C(x*A(x)^3) / (1 - x*A(x)^3).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((serreverse(x*((1-x)*2*x/(1-sqrt(1-4*x)))^3)/x)^(1/3))

Crossrefs

Cf. A381817, A381818, A381820.

Cf. A000108, A381773.

Sequence in context: A138014 A206988 A217360 * A371669 A363311 A052606

Adjacent sequences: A381816 A381817 A381818 * A381820 A381821 A381822

Keyword

nonn

Author

Seiichi Manyama, Mar 07 2025

Status

approved