A080835 - OEIS

%I #9 Oct 05 2013 06:15:22

%S 1,1,3,19,169,1761,22171,325123,5416209,101177569,2093489011,

%T 47501861331,1172566502713,31276078199809,896253254128779,

%U 27456289993445251,895308888305467681,30958452403586027073

%N E.g.f.: exp( x/( 1 - x - x^2 - x^3 ) ).

%H Vincenzo Librandi, <a href="/A080835/b080835.txt">Table of n, a(n) for n = 0..200</a>

%F E.g.f.: exp( x/( 1 - x - x^2 - x^3 ) ).

%F a(n) = (2*n-1)*a(n-1) + (n-2)*(n-1)*a(n-2) + (n-2)*(n-1)*a(n-3) - (n-3)*(n-2)*(n-1)*(3*n-14)*a(n-4) - 2*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5) - (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6). - _Vaclav Kotesovec_, Oct 02 2013

%F a(n) ~ 11^(3/4) * exp((5*r - 3 + 4*sqrt(22*(3+r)*(1+2*r)*n))/44 - n) * n^(n-1/4) * ((3+r)*(1+2*r))^(1/4) / (r^n * 2^(1/4) * sqrt((-3+(9-4*r)*r)*(4+r*(3+2*r))*(14+r*(7+2*r))*(1+r*(2+3*r)))), where r = ((17+3*sqrt(33))^(1/3) - 2/(17+3*sqrt(33))^(1/3) - 1)/3 = 0.543689012692... is the root of the equation -1 + r + r^2 + r^3 = 0. - _Vaclav Kotesovec_, Oct 02 2013

%t CoefficientList[Series[E^(x/(1-x-x^2-x^3)), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 02 2013 *)

%K easy,nonn

%O 0,3

%A _Emanuele Munarini_, Mar 28 2003

%E Corrected name, _Joerg Arndt_, Oct 02 2013