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 A216585 #8 Nov 21 2024 16:20:16
%S A216585 1,2,11,66,485,3842,32712,291568,2697610,25679316,250190125,
%T A216585 2484270622,25062816127,256275246582,2650947762450,27697861115740,
%U A216585 291943603838698,3101066786857876,33167191013319532,356924515784037128,3862299973917286526,42003704374124712172
%N A216585 G.f.: exp( Sum_{n>=1} A000984(n)*A002426(n)*x^n/n ), where A000984 is the central binomial coefficients and A002426 is the central trinomial coefficients.
%F A216585 Logarithmic derivative yields A216584.
%e A216585 G.f.: A(x) = 1 + 2*x + 11*x^2 + 66*x^3 + 485*x^4 + 3842*x^5 + 32712*x^6 +...
%e A216585 such that
%e A216585 log(A(x)) = 2*1*x + 6*3*x^2/2 + 20*7*x^3/3 + 70*19*x^4/4 + 252*51*x^5/5 + 924*141*x^6/6 +...+ A000984(n)*A002426(n)*x^n/n +...
%o A216585 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,binomial(2*m,m)*polcoeff((1+x+x^2)^m,m)*x^m/m+x*O(x^n))),n)}
%o A216585 for(n=0,30,print1(a(n),", "))
%Y A216585 Cf. A216584, A216586, A002426, A000984.
%K A216585 nonn
%O A216585 0,2
%A A216585 _Paul D. Hanna_, Sep 09 2012