A370926 - OEIS

%I #9 Mar 06 2024 08:00:09

%S 1,1,2,6,28,220,2520,34510,519680,8527680,154831600,3151456000,

%T 71830281600,1809141934600,49559087177600,1459865188782000,

%U 45970426027926400,1543274016213529600,55120521154277779200,2088917638216953544000,83717918489664018560000

%N Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*exp(x^3/6)) ).

%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)} (n-3*k)^k * binomial(n+1,n-3*k)/(6^k * k!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x*exp(x^3/6)))/x))

%o (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k*binomial(n+1, n-3*k)/(6^k*k!))/(n+1);

%Y Cf. A161633, A370889.

%Y Cf. A365287.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 05 2024