A026773 a(n) = T(2n-1,n-1), T given by A026769. Also T(2n+1,n+1), T given by A026780.

1, 4, 17, 76, 352, 1674, 8129, 40156, 201236, 1020922, 5234660, 27089726, 141335846, 742712598, 3927908193, 20891799036, 111688381228, 599841215226, 3234957053984, 17512055200470, 95125188934942, 518340392855286, 2832580291316092, 15520177744727766

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

From Vladeta Jovovic, Nov 23 2003: (Start)

a(n) = A006318(n) - A000108(n).

G.f.: (sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2. (End)

From Paul Barry, May 19 2005: (Start)

a(n) = Sum_{k=0..n} C(n+k+1, n+1)*C(n+1, k)/(k+1).

a(n) = Sum_{k=0..n+1} C(n+2, k)*C(n+k, n+1)/(n+2). (End)

D-finite with recurrence n*(n+1)*a(n) -n*(11*n-7)*a(n-1) +(37*n^2-95*n+54)*a(n-2) +(-49*n^2+269*n-354)*a(n-3) +6*(9*n^2-71*n+138)*a(n-4) -4*(2*n-9)*(n-5)*a(n-5)=0. - R. J. Mathar, Aug 05 2021

Maple

seq(coeff(series((sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2, x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 01 2019

Mathematica

Rest@CoefficientList[Series[(Sqrt[1-4*x] - Sqrt[1-6*x+x^2])/(2*x) -1/2, {x, 0, 30}], x] (* G. C. Greubel, Nov 01 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2) \\ G. C. Greubel, Nov 01 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (Sqrt(1-4*x) - Sqrt(1-6*x+x^2))/(2*x) -1/2 )); // G. C. Greubel, Nov 01 2019
(Sage)
def A026773_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((sqrt(1-4*x) - sqrt(1-6*x+x^2))/(2*x) -1/2).list()
a=A026773_list(30); a[1:] # G. C. Greubel, Nov 01 2019
(GAP) List([0..30], n-> Sum([0..n], k-> Binomial(n+1, k)*Binomial(n+k+1, n+1)/(k+1) )); # G. C. Greubel, Nov 01 2019

Crossrefs

Cf. A026769, A026770, A026771, A026772, A026774, A026775, A026776, A026777, A026778, A026779.

Sequence in context: A290914 A117439 A081910 * A081186 A239204 A005572

Adjacent sequences: A026770 A026771 A026772 * A026774 A026775 A026776

Keyword

nonn

Author

Clark Kimberling

Status

approved