A080834 E.g.f. exp( x/(1 - x - x^2) ) / (1 - x - x^2).

1, 2, 9, 58, 485, 4986, 60517, 846434, 13384233, 235915570, 4583337761, 97257637962, 2237249019469, 55438067438378, 1471848284860605, 41673308546595826, 1253228243522934737, 39886741017817705314

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

D-finite with recurrence a(n) = 2*n*a(n-1) + (n-1)^2*a(n-2) - 2*(n-2)^2*(n-1)*a(n-3) - (n-3)*(n-2)^2*(n-1)*a(n-4). - Vaclav Kotesovec, Sep 29 2013

a(n) ~ 5^(-3/8)*sqrt(7+3*sqrt(5))/2 * ((1+sqrt(5))/2)^(n-1)* exp(2*sqrt(n)/5^(1/4)-n-1/10) * n^(n+1/4) * (1 + sqrt(-73/600 + 293329/(288000*sqrt(5)))/sqrt(n)). - Vaclav Kotesovec, Sep 29 2013

Mathematica

CoefficientList[Series[E^(x/(1-x-x^2))/(1-x-x^2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 29 2013 *)

Crossrefs

Sequence in context: A132608 A361598 A247329 * A059115 A277358 A156129

Adjacent sequences: A080831 A080832 A080833 * A080835 A080836 A080837

Keyword

easy,nonn

Author

Emanuele Munarini, Mar 28 2003

Status

approved