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A370984
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2*exp(x)) ).
3
1, 0, 2, 6, 84, 860, 14430, 257082, 5678456, 140241096, 3952791450, 123539438990, 4266378769092, 160943793753756, 6592371152535350, 291260465060881890, 13809548247503299440, 699362685890810753552, 37679514498664685654706
OFFSET
0,3
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} k^(n-2*k) * (n+k)!/(k! * (n-2*k)!).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2*exp(x)))/x))
(PARI) a(n) = sum(k=0, n\2, k^(n-2*k)*(n+k)!/(k!*(n-2*k)!))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 06 2024
STATUS
approved