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%I #13 May 10 2013 12:45:02
%S 1,2,3,5,8,14,24,44,79,149,275,527,989,1913,3629,7061,13496,26366,
%T 50676,99296,191674,376430,729146,1434578,2786656,5490812,10691112,
%U 21091712,41150012,81266612,158825372,313942892,614483087,1215563477
%N Column 2 of the array m(i,1)=m(1,j)=1 m(i,j)=m(i-1,j-1)+m(i-1,j+1) (a(n)=m(n,2)).
%C Partial sums of A001405, to which an additional leading 1 is added. - _Paul Barry_, Oct 12 2004
%F G.f.: 1/2*x*(((1+2*x)/(1-2*x))^(1/2)-1)/(1-x)-1. - _Vladeta Jovovic_, Jan 15 2004
%F G.f. : (sqrt(1+2x)+1/sqrt(1-2x))/((1-x)(sqrt(1+2x)+sqrt(1-2x))); a(n)=1+sum{k=0..n, binomial(n-1, floor((n-1)/2)}. - _Paul Barry_, Oct 12 2004
%F Conjecture: (-n+1)*a(n) +(n+1)*a(n-1) +2*(2*n-7)*a(n-2) +4*(-n+3)*a(n-3)=0. - _R. J. Mathar_, Nov 26 2012
%Y Cf. A036256.
%K easy,nonn
%O 1,2
%A _Benoit Cloitre_, Jul 30 2002
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