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 A078737 #6 Mar 30 2012 18:39:11 %S A078737 1,1,2,3,17,20,37,353,390,743,10049,10792,20841,365089,385930,751019, %T A078737 16157329,16908348,33065677,843550273,876615950,1720166223, %U A078737 50761436417,52481602640,103243039057,3459501891521,3562744930578,7022246822099 %N A078737 Denominators of convergents to sqrt(e). %F A078737 Let y(n, x)=sum(k=0, n, (n+k)!*(x/2)^k/((n-k)!*k!)) then : a(3*n-1)=(1/2)*(|y(n, -4)|- |y(n-1, -4)|); a(3*n)=(1/2)*(|y(n, -4)|+ |y(n-1, -4)|); a(3*n+1)=|y(n, -4)| %o A078737 (PARI) a(n)=component(component(contfracpnqn(contfrac(exp(1/2),n)),1),2) %Y A078737 Cf. A058281, A078736, A065919. %K A078737 frac,nonn %O A078737 1,3 %A A078737 _Benoit Cloitre_, Dec 20 2002