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%I #13 Feb 28 2014 03:32:08
%S 1,2,7,25,111,571,3468,24340,194883,1754203,17542668,192970372,
%T 2315646974,30103414758,421447816520,6321717264184,101147476266147,
%U 1719507096590035,30951127738776012,588071427037006372
%N a(n) = n!*sum( i+j<=n, 1/i!/j! ) for 0 <= i <= j < n.
%H Vincenzo Librandi, <a href="/A076176/b076176.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: (exp(2*x)+I_0(2*x))/(2-2*x).
%F 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
%F a(n) ~ c * n!, where c = (exp(2) + BesselI(0,2)) / 2 = 4.83432070063335874733381595... - _Vaclav Kotesovec_, Feb 25 2014
%t Table[n!*Sum[Boole[i+j <= n]/(i!*j!), {i, 0, n}, {j, i, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Feb 25 2014 *)
%o (PARI) a(n)=if(n<0,0,n!*sum(i=0,n,sum(j=i,n-i,1/i!/j!)))
%o (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))
%Y Cf. A076177.
%K nonn
%O 0,2
%A _Benoit Cloitre_, Nov 01 2002
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