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 (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 *)
PROG
(Magma)
A064059:= func< n | (n+1)*Binomial(n+12, 5)/6 >;
[A064059(n): n in [0..40]]; // G. C. Greubel, Sep 27 2024
(SageMath)
def A064059(n): return (n+1)*binomial(n+12, 5)//6
[A064059(n) for n in range(41)] # G. C. Greubel, Sep 27 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 13 2001
STATUS
approved