A027911 - OEIS

%I #24 Nov 28 2021 12:36:27

%S 1,3,15,77,414,2277,12727,71955,410346,2355962,13599915,78855339,

%T 458917850,2679183405,15683407785,92022516525,541050073146,

%U 3186886397310,18801598011274,111083331666918,657153430251396,3892199032434105,23077435617920925,136963282273730613,813597690808666386

%N a(n) = T(2*n+1,n), with T given by A027907.

%F a(n) = GegenbauerPoly(n,-2*n-1,-1/2). - _Emanuele Munarini_, Oct 20 2016

%F G.f.: g/(1-g-3*g^2), where g = x times the g.f. of A143927. - _Mark van Hoeij_, Nov 16 2011

%F 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 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 Table[GegenbauerC[n, -2 n - 1, -1/2], {n, 0, 100}] (* _Emanuele Munarini_, Oct 20 2016 *)

%o (Maxima) makelist(ultraspherical(n,-2*n-1,-1/2),n,0,12); /* _Emanuele Munarini_, Oct 20 2016 */

%o (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 Cf. A027907, A143927.

%K nonn

%O 0,2

%A _Clark Kimberling_

%E More terms from _Joerg Arndt_, Oct 20 2016