A294190 Expansion of e.g.f. exp(3*(1/(1-x)^3 - 1)).

1, 9, 117, 1881, 35505, 763209, 18309861, 483213033, 13876068609, 429885495945, 14269174133301, 504579048629049, 18917482749919857, 748904109963227721, 31194958415494252005, 1363010131166317306569, 62300347592864208824961

Offset: 0

Author

Seiichi Manyama, Oct 24 2017

Keywords

• nonn
• changed

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..410

Crossrefs

Column k=3 of A294188.

Cf. A202826.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[3(1/(1-x)^3-1)],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Mar 03 2018 *)

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(3*(1/(1-x)^3-1))))

Formula

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

From Vaclav Kotesovec, Aug 28 2025: (Start)

a(n) = (4*n+5)*a(n-1) - 6*(n-2)*(n-1)*a(n-2) + 4*(n-3)*(n-2)*(n-1)*a(n-3) - (n-4)*(n-3)*(n-2)*(n-1)*a(n-4).

a(n) ~ 3^(1/4) * exp(-9/4 + 5*sqrt(3)*n^(1/4)/8 + 3*sqrt(n)/2 + 4*n^(3/4)/sqrt(3) - n) * n^(n - 1/8)/2 * (1 + 1333*sqrt(3)/(2560*n^(1/4))). (End)