A380043 E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)^3) )^(1/3).

1, 1, 6, 73, 1364, 34585, 1110406, 43200535, 1975744856, 103892750209, 6176282882570, 409635957376591, 29988473838531748, 2402004132488328433, 208956515057627326094, 19619264794744128427495, 1977503574407863125008816, 212975277029523353673126529, 24408338689788753822318157330

Offset: 0

Author

Seiichi Manyama, Jan 10 2025

Keywords

• nonn

Crossrefs

Cf. A380039, A380041.

Cf. A161633, A380042.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x/(1+3*x*exp(x)))/x)^(1/3)))

PARI

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

Formula

E.g.f.: ( (1/x) * Series_Reversion(x/(1 + 3*x*exp(x))) )^(1/3).

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