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 A198952 #16 May 06 2012 23:19:33
%S A198952 1,1,3,45,3267,991845,1155605211,4910640919821,73614877173054099,
%T A198952 3802910817051064124469,665332303024345700007225099,
%U A198952 388955052253927480089824057425437,751710022839628223241451188902204177091
%N A198952 G.f.: Sum_{n>=0} n! * 3^(n*(n-1)/2) * x^n / Product_{k=1..n} (1 + k*3^k*x).
%C A198952 Compare the g.f. to the identities:
%C A198952 (1) 1/(1-x) = Sum_{n>=0} n! * x^n / Product_{k=1..n} (1 + k*x).
%C A198952 (2) 1+x = Sum_{n>=0} 3^(n*(n-1)/2) * x^n / Product_{k=1..n} (1 + 3^k*x).
%e A198952 G.f.: A(x) = 1 + x + 3*x^2 + 45*x^3 + 3267*x^4 + 991845*x^5 + 1155605211*x^6 +...
%e A198952 such that
%e A198952 A(x) = 1 + x/(1+3*x) + 2!*3^1*x^2/((1+1*3*x)*(1+2*9*x)) + 3!*3^3*x^3/((1+1*3*x)*(1+2*9*x)*(1+3*27*x)) + 4!*3^6*x^4/((1+1*3*x)*(1+2*9*x)*(1+3*27*x)*(1+4*81*x)) +...
%o A198952 (PARI) {a(n)=polcoeff(sum(m=0,n,m!*3^(m*(m-1)/2)*x^m/prod(k=1,m,1+k*3^k*x +x*O(x^n))),n)}
%o A198952 for(n=0,20,print1(a(n),", "))
%Y A198952 Cf. A182507.
%K A198952 nonn
%O A198952 0,3
%A A198952 _Paul D. Hanna_, May 06 2012