OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
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 *)
PROG
(Magma)
A064061:= func< n | (n+1)*Binomial(n+14, 6)/7 >;
[A064061(n): n in [0..40]]; // G. C. Greubel, Sep 28 2024
(SageMath)
def A064061(n): return (n+1)*binomial(n+14, 6)//7
[A064061(n) for n in range(41)] # G. C. Greubel, Sep 28 2024
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Wolfdieter Lang, Sep 13 2001
STATUS
approved