A370930 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x^2/2)) ).
1, 1, 4, 33, 408, 6735, 139680, 3494715, 102486720, 3448812465, 131019940800, 5547190409145, 259025571826560, 13225167056035935, 733000949195074560, 43830500433645600675, 2812624056522882201600, 192798872614347464289825
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x^2/2)))/x)) -
PARI
a(n) = sum(k=0, n\2, (n-2*k)^k*(2*n-2*k)!/(2^k*k!*(n-2*k)!))/(n+1);
Formula
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)!).