A376345 - OEIS

%I #14 Sep 21 2024 07:45:23

%S 1,0,0,6,0,60,2880,840,201600,7998480,12700800,1816547040,67898476800,

%T 311359688640,35628798965760,1317155266627200,12924530383564800,

%U 1308998905659244800,49463008450023168000,863080350836537433600,81264621182097120768000,3227330594664084337228800,87828327888763088096870400

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

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

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (2*n-2*k)! * Stirling2(k,n-2*k)/k!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^2)-1)))/x))

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

%Y Cf. A370988, A376347.

%Y Cf. A370989, A375588.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Sep 21 2024