%I #15 Jul 17 2020 22:58:58
%S -1,-1,-1,7,127,1711,23231,334391,5144063,84149983,1446872959,
%T 25661798119,454494403199,7489030040207,89680375568447,
%U -759618144120809,-127049044802971649,-7480338932613448769,-369274690558092738817,-17262533154073740329017
%N E.g.f.: -exp(-x/(1-2*x))/(1-2*x).
%C Polynomials in A021009 evaluated at 2.
%H Vaclav Kotesovec, <a href="/A025166/b025166.txt">Table of n, a(n) for n = 0..400</a>
%F Conjecture: a(n) + (-4*n+3)*a(n-1) + 4*(n-1)^2*a(n-2) = 0. - _R. J. Mathar_, Feb 05 2013
%F a(n) = -(-2)^n*KummerU(-n, 1, 1/2). - _Peter Luschny_, Feb 12 2020
%F Sum_{n>=0} a(n) * x^n / (n!)^2 = -exp(2*x) * BesselJ(0,2*sqrt(x)). - _Ilya Gutkovskiy_, Jul 17 2020
%p a := n -> -(-2)^n*KummerU(-n, 1, 1/2):
%p seq(simplify(a(n)), n=0..19); # _Peter Luschny_, Feb 12 2020
%t Table[ -n! 2^n LaguerreL[ n, 1/2 ], {n, 0, 12} ]
%Y Cf. A025167, A025168.
%K sign
%O 0,4
%A _Wouter Meeussen_
%E Corrected and extended by _Vladeta Jovovic_, Jan 29 2003