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

0,2

Links

Table of n, a(n) for n=0..24.

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

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 *)

Prog

(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

Crossrefs

Cf. A027907, A143927.

Sequence in context: A037654 A074561 A026115 * A125700 A227954 A104530

Adjacent sequences: A027908 A027909 A027910 * A027912 A027913 A027914

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Joerg Arndt, Oct 20 2016

Status

approved