A376390 Expansion of e.g.f. (1/x) * Series_Reversion( x*(2 - exp(x))^3 ).

1, 3, 33, 666, 19923, 795438, 39849549, 2405748978, 170114699247, 13796351753670, 1262691211748865, 128760309960844554, 14478116911623185163, 1779761344294187865198, 237465809999666515842261, 34179385495053448088261154, 5279029838285444642785757415, 870905593631158913782753290198

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Index entries for reversions of series

Formula

E.g.f. A(x) satisfies A(x) = 1/(2 - exp(x*A(x)))^3.

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A367135.

a(n) = (3/(3*n+3)!) * Sum_{k=0..n} (3*n+k+2)! * Stirling2(n,k).

a(n) ~ 3^(4*n+3) * LambertW(2*exp(1/3)/3)^(3*n+3) * n^(n-1) / (sqrt(1 + LambertW(2*exp(1/3)/3)) * 2^(3*n+3) * exp(n) * (3*LambertW(2*exp(1/3)/3) - 1)^(4*n+3)). - Vaclav Kotesovec, Feb 02 2026

Mathematica

Table[3/(3*n+3)! * Sum[(3*n+k+2)! * StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 02 2026 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(2-exp(x))^3)/x))
(PARI) a(n) = 3*sum(k=0, n, (3*n+k+2)!*stirling(n, k, 2))/(3*n+3)!;

Crossrefs

Cf. A367135, A376391.

Cf. A226515.

Sequence in context: A336636 A364242 A390106 * A395079 A376393 A380666

Adjacent sequences: A376387 A376388 A376389 * A376391 A376392 A376393

Keyword

nonn

Author

Seiichi Manyama, Sep 22 2024

Status

approved