A116408 E.g.f. exp(x)*(Bessel_I(2,2*x) - Bessel_I(3,2*x) + Bessel_I(4,2*x)).
0, 0, 1, 2, 7, 20, 61, 182, 546, 1632, 4875, 14542, 43340, 129064, 384111, 1142610, 3397656, 10100448, 30020283, 89213094, 265096455, 787695636, 2340488535, 6954401762, 20664628438, 61406952800, 182488572045, 542358944946
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
-
Mathematica
With[{nn=30},CoefficientList[Series[Exp[x](BesselI[2,2x]-BesselI[3,2x ]+ BesselI[ 4,2x]),{x,0,nn}],x]Range[0,nn]!] (* Harvey P. Dale, Mar 13 2013 *)
Formula
a(n) = Sum{k=0..n} C(n,k)*(-1)^k*(C(k+1,k/2-1)*(1+(-1)^k)/2 + C(k,(k-1)/2-1)*(1-(-1)^k)/2).
Conjecture: 2*(n+4)*(n-23)*a(n) + 2*(n^2+64n+79)*a(n-1) +(-59n^2+232n+740)*a(n-2) +(64n^2-585n+1019)*a(n-3) +3(n-3)*(41n-124)*a(n-4)=0. - R. J. Mathar, Dec 10 2011
Shorter recurrence: (n-2)*(n+4)*(3*n^2-5*n+36)*a(n) = n*(6*n^3-n^2+70*n-139)*a(n-1) + 3*(n-1)*n*(3*n^2+n+34)*a(n-2) - Vaclav Kotesovec, Jun 26 2013
a(n) ~ 3^(n+1/2)/(2*sqrt(Pi*n)). - Vaclav Kotesovec, Jun 26 2013
Comments