A144576 E.g.f.: exp(1-sqrt(1-2*x-4*x^2)).

1, 1, 6, 31, 301, 3426, 51751, 926731, 19691106, 479961901, 13256384851, 408621822126, 13915350562081, 518741273626681, 21013220503491126, 919071064063596151, 43167975952565245501, 2167078807061679282306, 115795155400715170458631, 6561750899663711363984851

Offset: 0

Author

N. J. A. Sloane, Jan 07 2009

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..377

Crossrefs

Cf. A001515, A144575.

Programs

Maple

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):
map(f, [$0..30]); # Robert Israel, Dec 31 2019

Mathematica

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 *)

Formula

a(n) ~ sqrt(5-sqrt(5))*(1+sqrt(5))^n*n^n/(2*n*exp(n-1)). - Vaclav Kotesovec, Jun 26 2013

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