A370930 - OEIS

%I #12 Mar 06 2024 07:59:51

%S 1,1,4,33,408,6735,139680,3494715,102486720,3448812465,131019940800,

%T 5547190409145,259025571826560,13225167056035935,733000949195074560,

%U 43830500433645600675,2812624056522882201600,192798872614347464289825

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

%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)} (n-2*k)^k * (2*n-2*k)!/(2^k * k! * (n-2*k)!).

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

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

%Y Cf. A213644, A370931.

%Y Cf. A358264.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 06 2024