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 A224734 #14 Mar 27 2025 08:44:59
%S A224734 1,4,26,216,2075,21916,247326,2930216,36028117,456089076,5910983050,
%T A224734 78100285784,1048696065394,14275198859304,196610207633100,
%U A224734 2735542102308752,38400942393884068,543307627503591440,7740605626606127512,110970838624540461472,1599834676405793089013
%N A224734 G.f.: exp( Sum_{n>=1} binomial(2*n,n)^2 * x^n/n ).
%C A224734 The o.g.f. A(x) is the fourth power of the o.g.f. of A158266. - _Peter Bala_, Jun 04 2015
%H A224734 Vaclav Kotesovec, <a href="/A224734/b224734.txt">Table of n, a(n) for n = 0..800</a>
%F A224734 Logarithmic derivative yields A002894.
%F A224734 a(n) ~ c * 16^n / n^2, where c = 0.4942922... - _Vaclav Kotesovec_, Mar 27 2025
%e A224734 G.f.: A(x) = 1 + 4*x + 26*x^2 + 216*x^3 + 2075*x^4 + 21916*x^5 + 247326*x^6 +...
%e A224734 where
%e A224734 log(A(x)) = 2^2*x + 6^2*x^2/2 + 20^2*x^3/3 + 70^2*x^4/4 + 252^2*x^5/5 + 924^2*x^6/6 + 3432^2*x^7/7 + 12870^2*x^8/8 +...+ A000984(n)^2*x^n/n +...
%t A224734 CoefficientList[Series[Exp[4*x*HypergeometricPFQ[{1, 1, 3/2, 3/2}, {2, 2, 2}, 16*x]], {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 27 2025 *)
%o A224734 (PARI) {a(n)=polcoeff(exp(sum(k=1,n,binomial(2*k,k)^2*x^k/k)+x*O(x^n)),n)}
%o A224734 for(n=0,20,print1(a(n),", "))
%Y A224734 Cf. A224732, A224735, A224736, A002894, A000984, A158266.
%K A224734 nonn
%O A224734 0,2
%A A224734 _Paul D. Hanna_, Apr 16 2013