A080835 E.g.f.: exp( x/( 1 - x - x^2 - x^3 ) ).

1, 1, 3, 19, 169, 1761, 22171, 325123, 5416209, 101177569, 2093489011, 47501861331, 1172566502713, 31276078199809, 896253254128779, 27456289993445251, 895308888305467681, 30958452403586027073

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

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

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

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

Mathematica

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

Crossrefs

Sequence in context: A105624 A238640 A349253 * A080836 A059280 A085295

Adjacent sequences: A080832 A080833 A080834 * A080836 A080837 A080838

Keyword

easy,nonn

Author

Emanuele Munarini, Mar 28 2003

Extensions

Corrected name, Joerg Arndt, Oct 02 2013

Status

approved