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A064059 Seventh column of Catalan triangle A009766. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 26 22:11 EDT 2022. Contains 357051 sequences. (Running on oeis4.)