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 A195736 #17 Mar 30 2012 18:37:29
%S A195736 1,2,21,568,29705,2573136,335201293,61480323584,15135660248913,
%T A195736 4823681315219200,1934425407465004421,954153609788873382912,
%U A195736 568125617688093236137561,402006917909739659429470208,333597313002114320208678928125
%N A195736 E.g.f.: x = Sum_{n>=1} a(n)*x^n/n! * exp(-n^2*x).
%C A195736 Compare e.g.f. to: x = Sum_{n>=1} n^(n-1)*x^n/n! * exp(-n*x), which generates coefficients for the series reversion of x*exp(-x).
%F A195736 G.f.: x = Sum_{n>=1} a(n)*x^n/(n*(1 + n^2*x)^n).
%F A195736 a(n) = n*A082157(n+1).
%e A195736 x = x*exp(-x) + 2*x^2/2!*exp(-4*x) + 21*x^3/3!*exp(-9*x) + 568*x^4/4!*exp(-16*x) + 29705*x^5/5!*exp(-25*x) +...+ a(n)*x^n/n!*exp(-n^2*x) +...
%e A195736 The coefficients a(n) also satisfy:
%e A195736 x = x/(1+x) + 2*x^2/(2*(1+4*x)^2) + 21*x^3/(3*(1+9*x)^3) + 568*x^4/(4*(1+16*x)^4) + 29705*x^5/(5*(1+25*x)^5) +...+ a(n)*x^n/(n*(1+n^2*x)^n) +...
%o A195736 (PARI) {a(n)=if(n<1,0,n!*polcoeff(x-sum(m=1,n-1,a(m)*x^m/m!*exp(-m^2*x+x*O(x^n))),n))}
%o A195736 (PARI) {a(n)=if(n<1,0,n*polcoeff(x-sum(m=1,n-1,a(m)*x^m/(m*(1+m^2*x+x*O(x^n))^m)),n))}
%Y A195736 Cf. A195737, A082157.
%K A195736 nonn
%O A195736 1,2
%A A195736 _Paul D. Hanna_, Sep 30 2011