OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
J. Adams and F. du Cloux, Algorithms for representation theory of real reductive groups, arXiv:math/0701166.
FORMULA
E.g.f.: exp(4*x+x^2). - corrected by Vaclav Kotesovec, Oct 19 2012
E.g.f. 2*(x+2)*(1 + (x+4)*x/(G(0)-x^2-4*x)) where G(k)= x^2 + 4*x + k + 1 - (x+4)*x*(k+1)/G(k+1); (continued fraction, Euler's 1st kind, 1-step). - Sergei N. Gladkovskii, Jul 12 2012
Recurrence: a(n) = 4*a(n-1) + 2*(n-1)*a(n-2). - Vaclav Kotesovec, Oct 19 2012
a(n) ~ 2^(n/2-1/2)*exp(2*sqrt(2*n)-n/2-2)*n^(n/2)*(1+7/6*sqrt(2)/sqrt(n)). - Vaclav Kotesovec, Oct 19 2012
MATHEMATICA
Rest[CoefficientList[Series[E^(4*x+x^2), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Oct 19 2012 *)
PROG
(PARI) x='x+O('x^66); Vec(serlaplace(2*(x+2)*exp(x*(x+4)))) /* Joerg Arndt, Jul 12 2012 */
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 01 2007
STATUS
approved