A027911 a(n) = T(2*n+1,n), with T given by A027907.

1, 3, 15, 77, 414, 2277, 12727, 71955, 410346, 2355962, 13599915, 78855339, 458917850, 2679183405, 15683407785, 92022516525, 541050073146, 3186886397310, 18801598011274, 111083331666918, 657153430251396, 3892199032434105, 23077435617920925, 136963282273730613, 813597690808666386

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A027907, A143927.

Programs

Maple

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

Mathematica

Table[GegenbauerC[n, -2 n - 1, -1/2], {n, 0, 100}] (* Emanuele Munarini, Oct 20 2016 *)

Maxima

makelist(ultraspherical(n,-2*n-1,-1/2),n,0,12); /* Emanuele Munarini, Oct 20 2016 */

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

Formula

a(n) = GegenbauerPoly(n,-2*n-1,-1/2). - Emanuele Munarini, Oct 20 2016

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

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

Extensions

More terms from Joerg Arndt, Oct 20 2016