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 A054443 #14 Mar 07 2024 14:41:03
%S A054443 1,4,14,40,109,276,682,1624,3810,8744,19868,44496,98941,217780,476786,
%T A054443 1036024,2241814,4823160,10342180,22076080,46994386,99673224,
%U A054443 210923364,445000560,937051684,1968204496,4127285688,8636324768,18045851165,37638105588,78404375362
%N A054443 Third convolution of A001405 (central binomial numbers).
%H A054443 Alois P. Heinz, <a href="/A054443/b054443.txt">Table of n, a(n) for n = 0..1000</a>
%F A054443 a(2*k) = (2*k+7)*4^(k+1)-binomial(2*(k+2), k+2)*(4*k+9)/2, a(2*k+1) = (k+4)*4^(k+2)-(k+3)*binomial(2*(k+3), k+3), k >= 0.
%F A054443 a(n) = A054336(n+3, 3) (fourth column of convolution triangle). G.f.: (1/(1-x-x^2*c(x^2)))^4, with c(x) the g.f. for the Catalan numbers A000108.
%F A054443 G.f.: (c(x/(2x-1))/(1-2x))^4. - _Michael Somos_, Jul 31 2005
%o A054443 (PARI) {a(n)=local(k);if(n<0, 0, k=n\2; if(n%2, (k+4)*4^(k+2)-(k+3)*binomial(2*(k+3),k+3), (2*k+7)*4^(k+1)-binomial(2*(k+2),k+2)*(4*k+9)/2 ))}
%Y A054443 Cf. A000108, A001405, A054336, A054442.
%K A054443 easy,nonn
%O A054443 0,2
%A A054443 _Wolfdieter Lang_, Mar 27 2000