A348468 Expansion of e.g.f. sqrt(exp(x)*(2-exp(x))).

1, 0, -1, -3, -10, -45, -271, -2058, -18775, -199335, -2410516, -32683563, -490870315, -8087188200, -144994236661, -2810079139143, -58536519252130, -1304198088413265, -30946462816602331, -779104979758256298, -20742005411397108595, -582214473250983046155, -17184302765073000634276

Offset: 0

Author

Michel Marcus, Oct 19 2021

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..425
• Feng Qi and Mark Daniel Ward, Closed-form formulas and properties of coefficients in Maclaurin's series expansion of Wilf's function, arXiv:2110.08576 [math.CO], 2021.

Crossrefs

Cf. A000629, A000918, A014304, A014307, A260701, A260902.

Programs

Mathematica

m = 22; Range[0, m]! * CoefficientList[Series[Sqrt[Exp[x]*(2 - Exp[x])], {x, 0, m}], x] (* Amiram Eldar, Oct 19 2021 *)

PARI

my(x='x+O('x^25)); Vec(serlaplace(sqrt(exp(x)*(2-exp(x)))))

Formula

a(n) ~ -sqrt(2) * n^(n-1) / (log(2)^(n - 1/2) * exp(n)). - Vaclav Kotesovec, Oct 21 2021