OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: (exp(2*x)+I_0(2*x))/(2-2*x).
Recurrence: n*a(n) = (n^2 + 2*n - 2)*a(n-1) - 2*(n-3)*(n-1)*a(n-2) - 4*(n-2)*(n+1)*a(n-3) + 8*(n-3)*(n-2)*a(n-4). - Vaclav Kotesovec, Feb 25 2014
a(n) ~ c * n!, where c = (exp(2) + BesselI(0,2)) / 2 = 4.83432070063335874733381595... - Vaclav Kotesovec, Feb 25 2014
MATHEMATICA
Table[n!*Sum[Boole[i+j <= n]/(i!*j!), {i, 0, n}, {j, i, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 25 2014 *)
PROG
(PARI) a(n)=if(n<0, 0, n!*sum(i=0, n, sum(j=i, n-i, 1/i!/j!)))
(PARI) a(n)=if(n<0, 0, n!*polcoeff((exp(2*x+x*O(x^n))+besseli(0, 2*x+x*O(x^n)))/(2-2*x), n))
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Nov 01 2002
STATUS
approved