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A064061 Eighth column of Catalan triangle A009766. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

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

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

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).

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

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Last modified November 13 13:15 EST 2018. Contains 317149 sequences. (Running on oeis4.)