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A026770 a(n) = T(2n,n), T given by A026769. 11
1, 2, 7, 28, 120, 538, 2493, 11854, 57558, 284392, 1426038, 7241356, 37173304, 192638992, 1006564439, 5297715628, 28061959428, 149491856978, 800425486692, 4305263668514, 23251846197766, 126044501870378, 685569373724964, 3740339567665558, 20463965229643218, 112250484320225118 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of lattice paths from (0,0) to (n,n) with steps (0,1), (1,0) and, when below the diagonal, (1,1). - Alois P. Heinz, Sep 14 2016

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

O.g.f.: 1/(1-x*(C(x)+S(x))), where C(x)=(1-sqrt(1-4x))/(2*x) is o.g.f. for A000108 and S(x)=(1-x-sqrt(1-6*x+x^2))/(2*x) is o.g.f. for A006318. - Max Alekseyev, Dec 02 2015

MAPLE

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

MATHEMATICA

T[n_, k_] := T[n, k] = Which[k==0 || k==n, 1, n==2 && k==1, 2, k<=(n-1)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], True, T[n-1, k-1] + T[n-1, k]];

a[n_] := T[2n, n];

Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 24 2019 *)

PROG

(PARI) { C = (1-sqrt(1-4*x+O(x^51)))/2/x; S = (1-x-sqrt(1-6*x+x^2 +O(x^51)))/2/x; Vec(1/(1-x*(C+S))) } /* Max Alekseyev, Dec 02 2015 */

(MAGMA) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(x + Sqrt(1-4*x) + Sqrt(1-6*x+x^2)) )); // G. C. Greubel, Nov 01 2019

(Sage)

def A026770_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( 2/(x + sqrt(1-4*x) + sqrt(1-6*x+x^2)) ).list()

A026770_list(30) # G. C. Greubel, Nov 01 2019

CROSSREFS

Cf. A000108, A006318, A026781, A104625, A109980.

Cf. A026769, A026771, A026772, A026773, A026774, A026775, A026776, A026777, A026778, A026779.

Sequence in context: A150656 A150657 A150658 * A241371 A010683 A276852

Adjacent sequences:  A026767 A026768 A026769 * A026771 A026772 A026773

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified February 24 09:40 EST 2020. Contains 332209 sequences. (Running on oeis4.)