A027913 T(n,[ n/2 ]), T given by A027907.

1, 1, 2, 3, 10, 15, 50, 77, 266, 414, 1452, 2277, 8074, 12727, 45474, 71955, 258570, 410346, 1481108, 2355962, 8533660, 13599915, 49402850, 78855339, 287134346, 458917850, 1674425300, 2679183405, 9792273690, 15683407785

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

The median coefficient in the expansion of (1 + x + x^2)^n. - Vladimir Reshetnikov, Nov 21 2020

Links

• Robert Israel, Table of n, a(n) for n = 0..2550

Crossrefs

Cf. A027907, A027908.

Programs

Maple

seq(simplify(GegenbauerC(floor(n/2),-n,-1/2)), n=0..100); # Robert Israel, Oct 20 2016

Mathematica

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

Maxima

makelist(ultraspherical(floor(n/2),-n,-1/2),n,0,12); /* Emanuele Munarini, Oct 18 2016 */

Formula

a(n) = GegenbauerC(floor(n/2), -n, -1/2). - Emanuele Munarini, Oct 18 2016

G.f.: g(t) = (1+(t+t^2)*A(t^2)+t^4*A(t^2)^2)/(1-t^2*A(t^2)-3*t^4*A(t^2)^2), where A(t) is the g.f. of A143927 and satisfies A(t) = [1 + x*A(t) + t^2*A(t)^2]^2. - Emanuele Munarini, Oct 20 2016