A370927 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x^2)) ).

1, 1, 4, 36, 480, 8460, 187200, 4998000, 156387840, 5614313040, 227520921600, 10275211679040, 511772590264320, 27870149349282240, 1647541857684602880, 105073768465758892800, 7191330561736409088000, 525746801445336504633600

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A213644, A370928.

Programs

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);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (n-2*k)^k * (2*n-2*k)!/(k! * (n-2*k)!).