A294189 E.g.f.: exp(2*(1/(1-x)^2 - 1)).

1, 4, 28, 256, 2848, 37024, 547936, 9064192, 165339904, 3290839552, 70870959616, 1640130678784, 40555349598208, 1066271901822976, 29684252411219968, 871864036043259904, 26931181039027879936, 872418396180001718272, 29564373329109844885504

Offset: 0

Author

Seiichi Manyama, Oct 24 2017

Keywords

• nonn
• changed

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..427

Crossrefs

Column k=2 of A294188.

Cf. A136658.

Programs

Mathematica

nmax = 20; CoefficientList[Series[E^(2*(1/(1-x)^2 - 1)), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Aug 28 2025 *)

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(2*(1/(1-x)^2-1))))

Formula

From Vaclav Kotesovec, Aug 28 2025: (Start)

a(n) = (3*n+1)*a(n-1) - 3*(n-2)*(n-1)*a(n-2) + (n-3)*(n-2)*(n-1)*a(n-3).

a(n) ~ 2^(1/3) * 3^(-1/2) * exp(-4/3 + 2^(1/3)*n^(1/3) + 3*2^(-1/3)*n^(2/3) - n) * n^(n - 1/6) * (1 + 19/(27*2^(1/3)*n^(1/3)) - 11/(3645*2^(2/3)*n^(2/3))). (End)