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

0,4

Comments

Third column in number triangle A116407.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

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 *)

Crossrefs

Sequence in context: A201967 A116950 A111017 * A015518 A014983 A083379

Adjacent sequences: A116405 A116406 A116407 * A116409 A116410 A116411

Keyword

easy,nonn

Author

Paul Barry, Feb 13 2006

Status

approved