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A117187
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Expansion of (1+x)c(x^2)/((1-x^2*c(x^2))sqrt(1-4x^2)), c(x) the g.f. of A000108.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Diagonal sums of triangle A117184. Also second column of triangle A117184.
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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: (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
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CROSSREFS
| Sequence in context: A019081 A059443 A097335 * A138767 A048282 A068592
Adjacent sequences: A117184 A117185 A117186 * A117188 A117189 A117190
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 01 2006
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