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 A172389 #2 Mar 30 2012 18:37:20
%S A172389 1,1,2,7,44,481,9272,310087,18164624,1843946881,326808099872,
%T A172389 100310221406407,53656068398769344,49686835289802328801,
%U A172389 80090696216400251499392,223445962168511596412895367
%N A172389 a(n) = Sum_{k=0..n} C(n,k)*3^(k*(n-k))/2^n.
%F A172389 O.g.f.: A(x) = Sum_{n>=0} 2*x^n/(2 - 3^n*x)^(n+1).
%F A172389 E.g.f.: E(x) = Sum_{n>=0} exp(3^n*x/2)*(x/2)^n/n!.
%F A172389 a(n) = A135079(n)/2^n.
%e A172389 O.g.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 44*x^4 + 481*x^5 + 9272*x^6 +...
%e A172389 A(x) = 2/(2-x) + 2*x/(2-3*x)^2 + 2*x^2/(2-3^2*x)^3 + 2*x^3/(2-3^3*x)^4 +...+ 2*x^n/(2-3^n*x)^(n+1) +...
%e A172389 E.g.f.: E(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 44*x^4/4! + 481*x^5/5! +...
%e A172389 E(x) = exp(x/2) + exp(3*x/2)*x/2 + exp(3^2*x/2)*(x/2)^2/2! + exp(3^3*x/2)*(x/2)^3/3! +...+ exp(3^n*x/2)*(x/2)^n/n! +...
%o A172389 (PARI) {a(n)=sum(k=0,n,binomial(n,k)*3^(k*(n-k)))/2^n}
%o A172389 (PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(3^k*x/2 +x*O(x^n))*(x/2)^k/k!), n)}
%o A172389 (PARI) {a(n)=polcoeff(sum(k=0, n, (x/2)^k/(1-3^k*x/2 +x*O(x^n))^(k+1)), n)}
%Y A172389 Cf. variants: A135079, A047863.
%K A172389 nonn
%O A172389 0,3
%A A172389 _Paul D. Hanna_, Feb 03 2010