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A076176
a(n) = n!*sum( i+j<=n, 1/i!/j! ) for 0 <= i <= j < n.
2
1, 2, 7, 25, 111, 571, 3468, 24340, 194883, 1754203, 17542668, 192970372, 2315646974, 30103414758, 421447816520, 6321717264184, 101147476266147, 1719507096590035, 30951127738776012, 588071427037006372
OFFSET
0,2
LINKS
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
Cf. A076177.
Sequence in context: A150533 A150534 A150535 * A188719 A103465 A103464
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Nov 01 2002
STATUS
approved