A064059 Seventh column of Catalan triangle A009766.

132, 429, 1001, 2002, 3640, 6188, 9996, 15504, 23256, 33915, 48279, 67298, 92092, 123970, 164450, 215280, 278460, 356265, 451269, 566370, 704816, 870232, 1066648, 1298528, 1570800, 1888887, 2258739, 2686866, 3180372, 3746990, 4395118, 5133856, 5973044

Offset

0,1

Links

Table of n, a(n) for n=0..32.

Richard K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article 00.1.6.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: (132-495*x+770*x^2-616*x^3+252*x^4-42*x^5)/(1-x)^7; numerator polynomial is N(2;5, x) from A062991.

a(n) = A009766(n+6, 6) = (n+1)*binomial(n+12,5)/6.

a(n) = binomial(n+13,6) - 2*binomial(n+12,5). - Zerinvary Lajos, Jul 19 2006

a(n) = A214292(n+11,5). - Reinhard Zumkeller, Jul 12 2012

From Amiram Eldar, Sep 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 25961/2134440.

Sum_{n>=0} (-1)^n/a(n) = 4160*log(2)/77 - 79917773/2134440. (End)

Maple

[seq(binomial(n+1, 6)-2*binomial(n, 5), n=12..55)]; # Zerinvary Lajos, Jul 19 2006

Mathematica

CoefficientList[Series[(42 z^5-252 z^4+616 z^3-770 z^2+495 z-132)/(z-1)^7, {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)

Crossrefs

Cf. A000096, A005586, A005587, A005557 (third to sixth column).

Sequence in context: A116154 A305067 A278128 * A244103 A248555 A253502

Adjacent sequences: A064056 A064057 A064058 * A064060 A064061 A064062

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 13 2001

Status

approved