A370931 - OEIS

%I #13 Mar 06 2024 07:59:44

%S 1,1,4,30,340,5180,99360,2300830,62473600,1946941920,68507714800,

%T 2686816932800,116225776497600,5497681373384200,282305750023897600,

%U 15640212734095950000,929908726447266966400,59061538103044360083200,3990922849835432102592000

%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) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (n-3*k)^k * (2*n-3*k)!/(6^k * k! * (n-3*k)!).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x^3/6)))/x))

%o (PARI) a(n) = sum(k=0, n\3, (n-3*k)^k*(2*n-3*k)!/(6^k*k!*(n-3*k)!))/(n+1);

%Y Cf. A213644, A370930.

%Y Cf. A358265.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 06 2024