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 A042941 #11 Apr 17 2014 06:40:55
%S A042941 1,13,110,765,4746,27314,149052,781725,3975730,19730150,95973956,
%T A042941 459145778,2165937060,10095323460,46566906872,212857023069,
%U A042941 965208806082,4345780250270,19442667426420,86489687956518
%N A042941 Convolution of Catalan numbers A000108 with A038845.
%C A042941 Also convolution of A018218(n+1), n >= 0, with A000302 (powers of 4); also convolution of A000346 with A002697.
%H A042941 Fung Lam, <a href="/A042941/b042941.txt">Table of n, a(n) for n = 0..1000</a>
%F A042941 a(n) = binomial(n+3, 2)*(4^(n+1) - A000984(n+3)/A000984(2)) / 2.
%F A042941 G.f.: c(x)/(1-4*x)^3, where c(x) is the g.f. for Catalan numbers.
%F A042941 Recurrence: (n+1)*a(n) = 128*(1-2*n)*a(n-4) + 32*(8*n-1)*a(n-3) - 24*(4*n+1)*a(n-2) + 2*(8*n+5)*a(n-1). - _Fung Lam_, Apr 13 2014
%F A042941 a(n) ~ 2^(2*n)*(n^2 - 8*n^(3/2)/(3*sqrt(Pi))). - _Fung Lam_, Apr 13 2014
%F A042941 Recurrence: n*(n+1)*a(n) = 2*n*(4*n+9)*a(n-1) - 8*(n+2)*(2*n+3)*a(n-2). - _Vaclav Kotesovec_, Apr 16 2014
%t A042941 CoefficientList[Series[(1-Sqrt[1-4*x])/(2*x*(1-4*x)^3), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 16 2014 *)
%K A042941 easy,nonn
%O A042941 0,2
%A A042941 _Wolfdieter Lang_