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

%I #8 Aug 06 2024 09:21:40

%S 1,2,6,30,240,2520,30600,413280,6168960,101666880,1842825600,

%T 36483955200,782548905600,18048500870400,444816333561600,

%U 11656620213638400,323500679915212800,9475966585948262400,292101319958063616000,9450373008137757696000

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

%F a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n+1,n-3*k)/k!.

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

%o (PARI) a(n) = n!*sum(k=0, n\3, binomial(n+1, n-3*k)/k!);

%Y Cf. A361595, A375227.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 06 2024