%I #18 Jan 30 2020 21:29:16
%S 1,1,6,31,301,3426,51751,926731,19691106,479961901,13256384851,
%T 408621822126,13915350562081,518741273626681,21013220503491126,
%U 919071064063596151,43167975952565245501,2167078807061679282306,115795155400715170458631,6561750899663711363984851
%N E.g.f.: exp(1-sqrt(1-2*x-4*x^2)).
%H Robert Israel, <a href="/A144576/b144576.txt">Table of n, a(n) for n = 0..377</a>
%F a(n) ~ sqrt(5-sqrt(5))*(1+sqrt(5))^n*n^n/(2*n*exp(n-1)). - _Vaclav Kotesovec_, Jun 26 2013
%F D-finite with recurrence: a(n) +(-2*n+3)*a(n-1) +(-4*n^2+16*n-13)*a(n-2) +4*(-2*n+3)*a(n-3) -16*(n-1)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Jan 23 2020
%p f:= gfun:-rectoproc({a(n+5) = 64*(n+3)*(n+2)*(n+1)*a(n)+48*(n+3)*(n+2)*a(n+1)+4*(n+3)*(4*n^2+12*n+11)*a(n+2)+(12*n^2+60*n+73)*a(n+3)-(2*n+1)*a(n+4), a(0) = 1, a(1) = 1, a(2) = 6, a(3) = 31, a(4) = 301}, a(n), remember):
%p map(f, [$0..30]); # _Robert Israel_, Dec 31 2019
%t With[{nn=20},CoefficientList[Series[Exp[1-Sqrt[1-2x-4x^2]],{x,0,nn}], x]Range[0,nn]!] (* _Harvey P. Dale_, Apr 30 2012 *)
%Y Cf. A001515, A144575.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jan 07 2009
|