A064061 Eighth column of Catalan triangle A009766.

429, 1430, 3432, 7072, 13260, 23256, 38760, 62016, 95931, 144210, 211508, 303600, 427570, 592020, 807300, 1085760, 1442025, 1893294, 2459664, 3164480, 4034712, 5101360, 6399888, 7970688, 9859575, 12118314, 14805180, 17985552, 21732542, 26127660, 31261516

Offset

0,1

Links

Table of n, a(n) for n=0..30.

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 (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = A009766(n+7, 7) = (n+1)*binomial(n+14, 6)/7.

G.f.: (429-2002*x+4004*x^2-4368*x^3+2730* x^4-924*x^5+132*x^6)/(1-x)^8; numerator polynomial is N(2;6, x) from A062991.

a(n) = C(n+13,7) - C(n+13,5). - Zerinvary Lajos, Nov 25 2006

a(n) = A214292(n+13,6). - Reinhard Zumkeller, Jul 12 2012

From Amiram Eldar, Sep 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 323171/88339680.

Sum_{n>=0} (-1)^n/a(n) = 7929257917/88339680 - 55552*log(2)/429. (End)

Maple

[seq(binomial(n, 7)-binomial(n, 5), n=13..37)]; # Zerinvary Lajos, Nov 25 2006

Mathematica

CoefficientList[Series[(132*z^6 - 924*z^5 + 2730*z^4 - 4368*z^3 + 4004*z^2 - 2002*z + 429)/(z - 1)^8, {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 16 2011 *)
Table[Binomial[n, 7]-Binomial[n, 5], {n, 13, 50}] (* or *) LinearRecurrence[ {8, -28, 56, -70, 56, -28, 8, -1}, {429, 1430, 3432, 7072, 13260, 23256, 38760, 62016}, 40] (* Harvey P. Dale, Sep 03 2015 *)

Crossrefs

Cf. A064059 (seventh column), A062991, A214292.

Sequence in context: A250330 A034278 A116870 * A244104 A115133 A090200

Adjacent sequences: A064058 A064059 A064060 * A064062 A064063 A064064

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 13 2001

Status

approved