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%I #9 Nov 21 2013 12:47:56
%S 1,2,3,5,28,33,61,582,643,1225,16568,17793,34361,601930,636291,
%T 1238221,26638932,27877153,54516085,1390779278,1445295363,2836074641,
%U 83691459952,86527534593,170218994545,5703754354578,5873973349123
%N Numerators of convergents to sqrt(e).
%F Let y(n, x)=sum(k=0, n, (n+k)!*(x/2)^k/((n-k)!*k!)) then : a(3*n)=(1/2)*(y(n, 4)+y(n-1, 4)); a(3*n+1)=y(n, 4); a(3*n+2)=(1/2)*(y(n+1, 4)-y(n, 4))
%t Numerator[Convergents[Sqrt[E],30]] (* _Harvey P. Dale_, Sep 23 2011 *)
%o (PARI) a(n)=component(component(contfracpnqn(contfrac(exp(1/2),n)),1),1)
%Y Cf. A058281, A078737, A065919.
%K frac,nonn
%O 1,2
%A _Benoit Cloitre_, Dec 20 2002
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