A375225 Expansion of e.g.f. exp( x^2/(1-x)^3 ) / (1-x)^3.

1, 3, 14, 96, 876, 9780, 127200, 1877400, 30947280, 563114160, 11202135840, 241655641920, 5614182826560, 139647350082240, 3700648372861440, 104032358410780800, 3090961262246457600, 96747013002684844800, 3180863885996673676800, 109570715078766355814400

Offset: 0

Author

Seiichi Manyama, Aug 06 2024

Keywords

• nonn

Crossrefs

Cf. A375172, A375224.

Cf. A351767.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[x^2/(1-x)^3]/(1-x)^3,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Nov 20 2024 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^2/(1-x)^3)/(1-x)^3))

PARI

a(n) = n!*sum(k=0, n\2, binomial(n+2+k, n-2*k)/k!);

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} binomial(n+2+k,n-2*k)/k!.