A180255 a(n) = n^2 * a(n-1) + n, a(0)=0.

0, 1, 6, 57, 916, 22905, 824586, 40404721, 2585902152, 209458074321, 20945807432110, 2534442699285321, 364959748697086236, 61678197529807573897, 12088926715842284483826, 2720008511064514008860865

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

Cf. A006040, A007526, A066998, A228229.

Sequence in context: A256016 A361291 A145170 * A371033 A034218 A034237

Adjacent sequences: A180252 A180253 A180254 * A180256 A180257 A180258

Keyword

nonn

Author

Groux Roland, Jan 17 2011

Status

approved