A375227 Expansion of e.g.f. exp( (x / (1-x))^3 ) / (1-x)^3.
1, 3, 12, 66, 504, 5040, 60840, 839160, 12882240, 217607040, 4018896000, 80691811200, 1750850640000, 40809559190400, 1016150162227200, 26898872647046400, 753882642267955200, 22291971504503500800, 693356807039126630400
Offset: 0
Keywords
Programs
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Mathematica
With[{nn=20},CoefficientList[Series[Exp[(x/(1-x))^3]/(1-x)^3,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 04 2025 *) -
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((x/(1-x))^3)/(1-x)^3)) -
PARI
a(n) = n!*sum(k=0, n\3, binomial(n+2, n-3*k)/k!);
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n+2,n-3*k)/k!.