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A180255 a(n)=n^2*a(n-1)+n, a(0)=0. 1
0, 1, 6, 57, 916, 22905, 824586, 40404721, 2585902152, 209458074321, 20945807432110, 2534442699285321, 364959748697086236, 61678197529807573897, 12088926715842284483826, 2720008511064514008860865 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

int(x^n*BesselI(0,2*x^(1/2)),x=0..1)=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

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

Sequence in context: A295238 A256016 A145170 * A034218 A034237 A291628

Adjacent sequences:  A180252 A180253 A180254 * A180256 A180257 A180258

KEYWORD

nonn

AUTHOR

Groux Roland, Jan 17 2011

STATUS

approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)