A117187 Expansion of (1+x)c(x^2)/((1-x^2*c(x^2))sqrt(1-4x^2)), c(x) the g.f. of A000108.

1, 1, 4, 4, 15, 15, 56, 56, 210, 210, 792, 792, 3003, 3003, 11440, 11440, 43758, 43758, 167960, 167960, 646646, 646646, 2496144, 2496144, 9657700, 9657700, 37442160, 37442160, 145422675, 145422675, 565722720

Offset: 0

Author

Paul Barry, Mar 01 2006

Keywords

• easy
• nonn

Comments

Diagonal sums of triangle A117184. Also second column of triangle A117184.

Formula

E.g.f.: dif(Bessel_I(1,2x)+Bessel_I(2,2x)+Bessel_I(3,2x),x);

a(n)=sum{k=0..n, C(n-k+1,n/2+1)(1+(-1)^n)/2+C(n-k, n/2+1/2)(1-(-1)^n)/2}.

Conjecture D-finite with recurrence: (n+4)*(31n-12)*a(n) +(37n^2+24n-156)*a(n-1) -4*(31n^2+81n+24)*a(n-2) -4*(37n+24)*(n-1)*a(n-3) =0. - R. J. Mathar, Dec 10 2011