
FORMULA

G.f.: 1/(1x2x^2/(16x24x^2/(114x80x^2/(122x168x^2/(130x288x^2/(1... (continued fraction).
a(n)= Sum_{k, 0<=k<=n} A111106(n,k)*2^(nk). [From Philippe Deléham, Nov 28 2009]
a(n) = upper left term of M^n, M = an infinite square production matrix as follows:
1, 1, 0, 0, 0, 0,...
2, 2, 2, 0, 0, 0,...
4, 4, 4, 4, 0, 0,...
6, 6, 6, 6, 6, 0,...
8, 8, 8, 8, 8, 8,...
...
(where the series (1,2,4,6,8,...) = A004277, positive even integers prefaced with a 1.)  Gary W. Adamson, Jul 19 2011
G.f. A(x) = 1+x/(G(0)x) where G(k)= 1  x*(2*k+2)/G(k+1)); (continued fraction, 1step). Sergei N. Gladkovskii, Oct 28 2012
