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

0,3

Comments

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

Links

Table of n, a(n) for n=0..30.

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

Crossrefs

Sequence in context: A287286 A271546 A325655 * A138767 A048282 A068592

Adjacent sequences: A117184 A117185 A117186 * A117188 A117189 A117190

Keyword

easy,nonn

Author

Paul Barry, Mar 01 2006

Status

approved