A025166 E.g.f.: -exp(-x/(1-2*x))/(1-2*x).

-1, -1, -1, 7, 127, 1711, 23231, 334391, 5144063, 84149983, 1446872959, 25661798119, 454494403199, 7489030040207, 89680375568447, -759618144120809, -127049044802971649, -7480338932613448769, -369274690558092738817, -17262533154073740329017

Offset: 0

Author

Wouter Meeussen

Keywords

• sign

Comments

Polynomials in A021009 evaluated at 2.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A025167, A025168.

Programs

Maple

a := n -> -(-2)^n*KummerU(-n, 1, 1/2):
seq(simplify(a(n)), n=0..19); # Peter Luschny, Feb 12 2020

Mathematica

Table[ -n! 2^n LaguerreL[ n, 1/2 ], {n, 0, 12} ]

Formula

Conjecture: a(n) + (-4*n+3)*a(n-1) + 4*(n-1)^2*a(n-2) = 0. - R. J. Mathar, Feb 05 2013

a(n) = -(-2)^n*KummerU(-n, 1, 1/2). - Peter Luschny, Feb 12 2020

Sum_{n>=0} a(n) * x^n / (n!)^2 = -exp(2*x) * BesselJ(0,2*sqrt(x)). - Ilya Gutkovskiy, Jul 17 2020

Extensions

Corrected and extended by Vladeta Jovovic, Jan 29 2003