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A370930
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x^2/2)) ).
2
1, 1, 4, 33, 408, 6735, 139680, 3494715, 102486720, 3448812465, 131019940800, 5547190409145, 259025571826560, 13225167056035935, 733000949195074560, 43830500433645600675, 2812624056522882201600, 192798872614347464289825
OFFSET
0,3
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)!).
PROG
(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);
CROSSREFS
Cf. A358264.
Sequence in context: A331794 A156132 A215364 * A213641 A343673 A343686
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 06 2024
STATUS
approved