A371019 - OEIS

%I #10 Mar 08 2024 07:59:55

%S 1,0,0,6,24,60,2280,35490,322896,6532344,175392720,3351681630,

%T 74021715240,2328376978356,68824597123464,1989994550546730,

%U 69687384248405280,2634948077918611440,98220733842576688416,3966108617957749165494,175679596523004500742840

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

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x^3*exp(x)))/x))

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

%Y Cf. A161633, A371018.

%Y Cf. A365287.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Mar 08 2024