A059348 Third diagonal of array in A059347.

2, 2, 3, 4, 7, 10, 19, 28, 56, 84, 174, 264, 561, 858, 1859, 2860, 6292, 9724, 21658, 33592, 75582, 117572, 266798, 416024, 950912, 1485800, 3417340, 5348880, 12369285, 19389690, 45052515, 70715340, 165002460, 259289580, 607283490

Offset: 2

Author

N. J. A. Sloane, Jan 27 2001

Keywords

• nonn
• changed

Comments

Same as A104722 except for leading term (both have rational g.f.s). - R. J. Mathar and Franklin T. Adams-Watters, May 19 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000
• F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 (1999), 73-112.

Crossrefs

Cf. A059347, A104722.

Programs

Mathematica

CoefficientList[Series[1 + ( (1 + x)*(1 - Sqrt[1 - 4*x^2])/(2*x^2))^2, {x, 0, 50}], x] (* G. C. Greubel, Jan 08 2017 *)

PARI

Vec( 1 + ( (1 + x)*(1 - sqrt(1 - 4*x^2))/(2*x^2))^2 + O(x^25)) \\ G. C. Greubel, Jan 08 2017

Formula

G.f.: 1 + ( (1 + x)*(1 - sqrt(1 - 4*x^2))/(2*x^2))^2. - G. C. Greubel, Jan 08 2017

a(n) ~ (9 + (-1)^n) * 2^(n - 3/2) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Aug 31 2025