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 A027911 #24 Nov 28 2021 12:36:27
%S A027911 1,3,15,77,414,2277,12727,71955,410346,2355962,13599915,78855339,
%T A027911 458917850,2679183405,15683407785,92022516525,541050073146,
%U A027911 3186886397310,18801598011274,111083331666918,657153430251396,3892199032434105,23077435617920925,136963282273730613,813597690808666386
%N A027911 a(n) = T(2*n+1,n), with T given by A027907.
%F A027911 a(n) = GegenbauerPoly(n,-2*n-1,-1/2). - _Emanuele Munarini_, Oct 20 2016
%F A027911 G.f.: g/(1-g-3*g^2), where g = x times the g.f. of A143927. - _Mark van Hoeij_, Nov 16 2011
%F A027911 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+1,k)*binomial(2*n+1-k,n-2*k). - _Emanuele Munarini_, Oct 20 2016
%p A027911 seq(add(binomial(j,2*j-2-3*n)*binomial(2*n+1,j),j=0...2*n+1),n=0..20); # _Mark van Hoeij_, May 12 2013
%t A027911 Table[GegenbauerC[n, -2 n - 1, -1/2], {n, 0, 100}] (* _Emanuele Munarini_, Oct 20 2016 *)
%o A027911 (Maxima) makelist(ultraspherical(n,-2*n-1,-1/2),n,0,12); /* _Emanuele Munarini_, Oct 20 2016 */
%o A027911 (PARI) a(n)=sum(j=0, 2*n+1, binomial(j, 2*j-2-3*n)*binomial(2*n+1, j)); \\ _Joerg Arndt_, Oct 20 2016
%Y A027911 Cf. A027907, A143927.
%K A027911 nonn
%O A027911 0,2
%A A027911 _Clark Kimberling_
%E A027911 More terms from _Joerg Arndt_, Oct 20 2016