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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, 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.
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 01 2006
STATUS
approved