This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A078736 #9 Nov 21 2013 12:47:56 %S A078736 1,2,3,5,28,33,61,582,643,1225,16568,17793,34361,601930,636291, %T A078736 1238221,26638932,27877153,54516085,1390779278,1445295363,2836074641, %U A078736 83691459952,86527534593,170218994545,5703754354578,5873973349123 %N A078736 Numerators of convergents to sqrt(e). %F A078736 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 A078736 Numerator[Convergents[Sqrt[E],30]] (* _Harvey P. Dale_, Sep 23 2011 *) %o A078736 (PARI) a(n)=component(component(contfracpnqn(contfrac(exp(1/2),n)),1),1) %Y A078736 Cf. A058281, A078737, A065919. %K A078736 frac,nonn %O A078736 1,2 %A A078736 _Benoit Cloitre_, Dec 20 2002