|
| |
|
|
A000973
|
|
Fermat coefficients.
(Formerly M4976 N2137)
|
|
3
|
|
|
|
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
|
|
|
REFERENCES
|
P. A. Piza, Fermat coefficients, Math. Mag., 27 (1954), 141-146.
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
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 1th 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.]
|
|
|
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
|
|
|
CROSSREFS
|
Cf. A053129.
Sequence in context: A108681 A108254 A174383 * A034266 A087661 A163717
Adjacent sequences: A000970 A000971 A000972 * A000974 A000975 A000976
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
EXTENSIONS
|
More terms from David W. Wilson, Oct 11 2000
|
|
|
STATUS
|
approved
|
| |
|
|
