A076176 a(n) = n!*sum( i+j<=n, 1/i!/j! ) for 0 <= i <= j < n.

1, 2, 7, 25, 111, 571, 3468, 24340, 194883, 1754203, 17542668, 192970372, 2315646974, 30103414758, 421447816520, 6321717264184, 101147476266147, 1719507096590035, 30951127738776012, 588071427037006372

Offset: 0

Author

Benoit Cloitre, Nov 01 2002

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A076177.

Programs

Mathematica

Table[n!*Sum[Boole[i+j <= n]/(i!*j!), {i, 0, n}, {j, i, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 25 2014 *)

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))

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