A377428 Expansion of e.g.f. (1/x) * Series_Reversion( x*(2 - exp(x))^4 ).

1, 4, 56, 1432, 54184, 2734104, 173032680, 13192623448, 1177932112040, 120610734752920, 13935516914366824, 1793837540679492312, 254604546529825454376, 39504947952102355425304, 6652925600854130108675048, 1208610940763303680263653464, 235601431979292206398224418216

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Index entries for reversions of series

Formula

E.g.f. A(x) satisfies A(x) = 1/(2 - exp(x*A(x)))^4.

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377424.

a(n) = (4/(4*n+4)!) * Sum_{k=0..n} (4*n+k+3)! * Stirling2(n,k).

a(n) ~ 2^(6*n+4) * LambertW(exp(1/4)/2)^(4*n+4) * n^(n-1) / (sqrt(1 + LambertW(exp(1/4)/2)) * exp(n) * (4*LambertW(exp(1/4)/2) - 1)^(5*n+4)). - Vaclav Kotesovec, Feb 02 2026

Mathematica

Table[4/(4*n+4)! * Sum[(4*n+k+3)! * 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))^4)/x))
(PARI) a(n) = 4*sum(k=0, n, (4*n+k+3)!*stirling(n, k, 2))/(4*n+4)!;

Crossrefs

Cf. A052894, A376389, A376390.

Cf. A377424, A377425.

Sequence in context: A183612 A377454 A377449 * A377429 A277038 A395382

Adjacent sequences: A377425 A377426 A377427 * A377429 A377430 A377431

Keyword

nonn

Author

Seiichi Manyama, Oct 28 2024

Status

approved