OFFSET
0,3
COMMENTS
Integral_{x=0..1} x^n*BesselI(0,2*x^(1/2)) dx = A006040(n)*BesselI(1,2) - a(n)*BesselI(0,2). An elementary consequence is the irrationality of BesselI(0,2)/BesselI(1,2).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..41
FORMULA
From Seiichi Manyama, Jan 05 2024: (Start)
a(n) = (n!)^2 * Sum_{k=0..n} k/(k!)^2.
a(n) = n * A228229(n-1) for n > 0. (End)
PROG
(PARI)
a(n)=if(n==0, 0, (n)^2*a(n-1)+(n));
for(n=0, 12, print1(a(n), ", ")); /* show terms */
(Maxima) a[0]:0$ a[n]:=n^2*a[n-1]+n$ makelist(a[n], n, 0, 15); /* Bruno Berselli, May 23 2011 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Groux Roland, Jan 17 2011
STATUS
approved