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A000973 Fermat coefficients.
(Formerly M4976 N2137)
4
1, 15, 99, 429, 1430, 3978, 9690, 21318, 43263, 82225, 148005, 254475, 420732, 672452, 1043460, 1577532, 2330445, 3372291, 4790071, 6690585, 9203634, 12485550, 16723070, 22137570, 28989675, 37584261, 48275865, 61474519 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

COMMENTS

a(n) = A258708(n,n-8). - Reinhard Zumkeller, Jun 23 2015

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, 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.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

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

MAPLE

A000973:=(z+1)*(z**2+6*z+1)/(z-1)**8; # conjectured by Simon Plouffe in his 1992 dissertation

A000973:=n->binomial(2*n-8, 7)/8; seq(A000973(n), n=8..40); # Wesley Ivan Hurt, Apr 16 2014

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

Cf. A053129.

Cf. A258708.

Sequence in context: A108681 A108254 A174383 * A034266 A087661 A242657

Adjacent sequences:  A000970 A000971 A000972 * A000974 A000975 A000976

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane, Apr 30 1991

EXTENSIONS

More terms from David W. Wilson, Oct 11 2000

STATUS

approved

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Last modified July 5 02:05 EDT 2015. Contains 259225 sequences.