A108308 Expansion of 1/(1-x^2*c(2x)), c(x) the g.f. of A000108.

1, 0, 1, 2, 9, 44, 245, 1462, 9157, 59368, 395033, 2682282, 18510561, 129451492, 915401757, 6534282398, 47020440413, 340733200288, 2484299720065, 18211441554706, 134145473550009, 992385470273692, 7370066147881413

Offset: 0

Author

Paul Barry, Jul 24 2005

Keywords

• easy
• nonn

Comments

Diagonal sums of A110510.

Formula

a(0)=1, a(n)=sum{k=0..floor(n/2), (k/(n-k))*C(2n-3k-1, n-2k)*2^(n-2k)}, n>0.

Conjecture: 2*(n-1)*a(n) +(41-17*n)*a(n-1) +4*(2n-5)*a(n-2) +(n-1)*a(n-3) +4*(5-2n)*a(n-4)=0. - R. J. Mathar, Dec 10 2011