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A370927
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x^2)) ).
3
1, 1, 4, 36, 480, 8460, 187200, 4998000, 156387840, 5614313040, 227520921600, 10275211679040, 511772590264320, 27870149349282240, 1647541857684602880, 105073768465758892800, 7191330561736409088000, 525746801445336504633600
OFFSET
0,3
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (n-2*k)^k * (2*n-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)))/x))
(PARI) a(n) = sum(k=0, n\2, (n-2*k)^k*(2*n-2*k)!/(k!*(n-2*k)!))/(n+1);
CROSSREFS
Sequence in context: A197446 A291313 A002690 * A094417 A349504 A354264
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 06 2024
STATUS
approved