OFFSET
0,2
LINKS
Shalosh B. Ekhad and Doron Zeilberger, Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type, arXiv preprint arXiv:1112.6207, 2011. See subpages for rigorous derivations of g.f., recurrence, asymptotics for this sequence. [From N. J. A. Sloane, Apr 07 2012]
FORMULA
G.f.: 1 + x + x*sqrt((1+2*x)/(1-2*x))= 1 + x + x/G(0), where G(k)= 1 - 2*x/(1 + 2*x/(1 + 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 26 2013
E.g.f.: 1 + x - (x*BesselI(1, 2*x)*(2 + Pi*(1 + 2*x)*StruveL(0, 2*x)) - x*(1 + 2*x)*BesselI(0, 2*x)*(2 + Pi*StruveL(1, 2*x)))/2. - Stefano Spezia, May 11 2024
MAPLE
a:= proc(n) option remember; `if`(n<3, [1, 2$3][n+1],
(2*a(n-1)+4*(n-3)*a(n-2))/(n-1))
end:
seq(a(n), n=0..39); # Alois P. Heinz, May 11 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 07 2012
STATUS
approved