A055142 Expansion of e.g.f.: exp(x)*sqrt(1-2x).

1, 0, -2, -8, -36, -224, -1880, -19872, -251888, -3712256, -62286624, -1171487360, -24402416192, -557542291968, -13861636770176, -372514645389824, -10759590258589440, -332386419622387712

Offset: 0

Author

Christian G. Bower, May 09 2000

Keywords

• sign

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A001147, A053871.

Column 0 of triangle A055141.

Programs

Mathematica

CoefficientList[Series[E^x*Sqrt[1-2*x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Mar 29 2014 *)

Sage

def A055142(n):
    @CachedFunction
    def h(n):
        return (-1)^n*2*(n-2)*abs(h(n-1)+h(n-2)) if n>1 else 1
    return -(-1)^(n+1)*h(n+1)
[A055142(n) for n in (0..17)]  # Peter Luschny, Nov 02 2012

Formula

a(n) ~ -2^(n-1/2) * n^(n-1) / exp(n-1/2). - Vaclav Kotesovec, Mar 29 2014

D-finite with recurrence: a(n) +2*(-n+1)*a(n-1) +2*(n-1)*a(n-2)=0. - R. J. Mathar, Jan 22 2020