OFFSET
8,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 8..1000
R. P. Loh, A. G. Shannon, and A. F. Horadam, Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients, Preprint, 1980.
P. A. Piza, Fermat coefficients, Math. Mag., 27 (1954), 141-146.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992.
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
a(n) = binomial(2*n-8, 7)/8.
G.f.: (x^8)*(1+7*x+7*x^2+x^3)/(1-x)^8.
G.f.: A(x) = (1+7*x+7*x^2+x^3)/(x-1)^8 = 1 + 45*x/(G(0)-45*x), |x|<1; if |x|>1, G(0)=45*x; G(k) = (k+1)*(2*k+3) + x*(k+5)*(2*k+9) - x*(k+1)*(k+6)*(2*k+3)*(2*k+11)/G(k+1); (continued fraction Euler's 1st kind, 1-step). - Sergei N. Gladkovskii, Jun 15 2012
a(n) = A258708(n,n-8). - Reinhard Zumkeller, Jun 23 2015
From Amiram Eldar, Nov 02 2025: (Start)
Sum_{n>=8} 1/a(n) = 6216/5 - 1792*log(2).
Sum_{n>=8} (-1)^n/a(n) = 1764/5 - 112*Pi. (End)
MAPLE
A000973:=(z+1)*(z**2+6*z+1)/(z-1)**8; # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
CoefficientList[Series[(1+7*x+7*x^2+x^3)/(1-x)^8, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 10 2012 *)
PROG
(Magma) [Binomial(2*n-8, 7)/8: n in [8..40]]; // Vincenzo Librandi, Apr 10 2012
(Haskell)
a000973 n = a258708 n (n - 8) -- Reinhard Zumkeller, Jun 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from David W. Wilson, Oct 11 2000
STATUS
approved