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A027911 a(n) = T(2*n+1,n), with T given by A027907. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A037654 A074561 A026115 * A227954 A104530 A297952

Adjacent sequences:  A027908 A027909 A027910 * A027912 A027913 A027914

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Joerg Arndt, Oct 20 2016

STATUS

approved

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Last modified November 17 12:09 EST 2018. Contains 317276 sequences. (Running on oeis4.)