A375902 E.g.f. satisfies A(x) = (2 - exp(x * A(x)^(1/2)))^2.

1, -2, 4, -2, -52, 358, 12, -25986, 247228, 821398, -52933300, 534428926, 6201248220, -271179578490, 2375560802188, 75726973445374, -2740636867741828, 14280527041851958, 1501820173046702796, -46939564687781824002, -67963035486950641508

Offset: 0

Author

Seiichi Manyama, Sep 02 2024

Keywords

• sign

Crossrefs

Cf. A007334, A097718, A375897.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace((serreverse(x/(2-exp(x)))/x)^2))

PARI

a(n) = 2*(n+1)!*sum(k=0, n, (-1)^k*stirling(n, k, 2)/(n-k+2)!);

Formula

E.g.f.: A(x) = ( (1/x) * Series_Reversion(x / (2 - exp(x))) )^2.

a(n) = 2 * (n+1)! * Sum_{k=0..n} (-1)^k * Stirling2(n,k)/(n-k+2)!.