A375227 - OEIS

%I #10 Aug 06 2024 09:22:41

%S 1,3,12,66,504,5040,60840,839160,12882240,217607040,4018896000,

%T 80691811200,1750850640000,40809559190400,1016150162227200,

%U 26898872647046400,753882642267955200,22291971504503500800,693356807039126630400

%N Expansion of e.g.f. exp( (x / (1-x))^3 ) / (1-x)^3.

%F a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n+2,n-3*k)/k!.

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

%o (PARI) a(n) = n!*sum(k=0, n\3, binomial(n+2, n-3*k)/k!);

%Y Cf. A361595, A375226.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 06 2024