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 A260630 #18 Apr 09 2017 03:40:17
%S A260630 -1,1,5,59,449,1417,16127,429697,437705,7549093,145103527,146489197,
%T A260630 3396112211,2442184933,7369048679,429556076057,13374954901367,
%U A260630 13427048535167,94315062045929,3500487562166393,3510273150915593,144285489968702713,6218562602767668259
%N A260630 Numerators of first derivatives of Catalan numbers (as continuous functions of n).
%C A260630 Let C(n) = 4^n*Gamma(n+1/2)/(sqrt(Pi)*Gamma(n+2)), then C'(n) = C(n)*(H(n-1/2) - H(n+1) + log(4)), where H(n) = Sum_{k>=1} (1/k-1/(n+k)) are harmonic numbers.
%H A260630 G. C. Greubel, <a href="/A260630/b260630.txt">Table of n, a(n) for n = 0..1000</a>
%F A260630 a(n) = numerator(d(n)), where d(n) satisfies recurrence: d(0) = -1, d(1) = 1/2, (n+1)^2*d(n) = 2*(4*n^2-2*n-1)*d(n-1) - 4*(2*n-3)^2*d(n-2).
%e A260630 For n = 3, C'(3) = 59/12, so a(3) = numerator(59/12) = 59.
%t A260630 Numerator@FunctionExpand@Table[CatalanNumber'[n] , {n, 0, 22}]
%Y A260630 Cf. A260631 (denominators).
%Y A260630 Cf. A000108, A001008, A074599.
%K A260630 sign,frac
%O A260630 0,3
%A A260630 _Vladimir Reshetnikov_, Nov 11 2015