A078736 Numerators of convergents to sqrt(e).
1, 2, 3, 5, 28, 33, 61, 582, 643, 1225, 16568, 17793, 34361, 601930, 636291, 1238221, 26638932, 27877153, 54516085, 1390779278, 1445295363, 2836074641, 83691459952, 86527534593, 170218994545, 5703754354578, 5873973349123
Offset: 1
Programs
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Mathematica
Numerator[Convergents[Sqrt[E],30]] (* Harvey P. Dale, Sep 23 2011 *)
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PARI
a(n)=component(component(contfracpnqn(contfrac(exp(1/2),n)),1),1)
Formula
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))