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 A199816 #7 Mar 14 2015 11:41:32
%S A199816 1,1,8,101,1639,30665,630225,13836981,319062453,7640441894,
%T A199816 188534274850,4767113222750,122998902095908,3228067183537455,
%U A199816 85960229675478804,2317956019913480326,63193008693741620771,1739473925024629613227,48292271242981605779173
%N A199816 G.f.: exp( Sum_{n>=1} A000984(n)*A000172(n)/4 * x^n/n ), which involves central binomial coefficients (A000984) and Franel numbers (A000172).
%C A199816 Sum_{k=0..n} C(n,k)^2 = A000984(n) defines central binomial coefficients.
%C A199816 Sum_{k=0..n} C(n,k)^3 = A000172(n) defines Franel numbers.
%C A199816 Compare to the g.f. of the Catalan numbers (A000108): exp(Sum_{n>=1} A000984(n)/2*x^n/n) and to the g.f. of A166991: exp(Sum_{n>=1} A000172(n)/2*x^n/n).
%F A199816 Convolution 4th power yields A199813.
%e A199816 G.f.: A(x) = 1 + x + 8*x^2 + 101*x^3 + 1639*x^4 + 30665*x^5 +...
%e A199816 where
%e A199816 log(A(x)) = 1*1*x + 3*5*x^2/2 + 10*28*x^3/3 + 35*173*x^4/4 + 126*1126*x^5/5 + 462*7592*x^6/6 +...+ A000984(n)/2*A000172(n)/2*x^n/n +...
%o A199816 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, binomial(2*m, m)/2*sum(k=0, m, binomial(m, k)^3)/2*x^m/m)+x*O(x^n)), n)}
%Y A199816 Cf. A199813, A166991, A000108, A181418, A000984, A000172.
%K A199816 nonn
%O A199816 0,3
%A A199816 _Paul D. Hanna_, Nov 11 2011