A000972 Fermat coefficients. (Formerly M4847 N2072)

1, 12, 66, 245, 715, 1768, 3876, 7752, 14421, 25300, 42287, 67860, 105183, 158224, 231880, 332112, 466089, 642341, 870922, 1163580, 1533939, 1997688, 2572780, 3279640, 4141382, 5184036, 6436782, 7932196, 9706503, 11799840, 14256528, 17125353, 20459857

Offset

7,2

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 = 7..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.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1,1,-6,15,-20,15,-6,1).

Formula

a(n) = A258708(n,n-7). - Reinhard Zumkeller, Jun 23 2015

G.f.: x^7*(1 + 6*x + 9*x^2 + 9*x^3 + 10*x^4 + 7*x^5 + 12*x^6 + 6*x^7 + 4*x^8) / ((1 - x)^7*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Colin Barker, Mar 28 2017

Maple

a := n->floor((2*n)*(2*n+1)*(2*n+2)*(2*n+3)*(2*n+4)*(2*n+5)/7!);

Mathematica

Table[Floor[((2*n)*(2*n+1)*(2*n+2)*(2*n+3)*(2*n+4)*(2*n+5)/7!)], {n, 1, 30}] (* Vincenzo Librandi, Apr 10 2012 *)
With[{c=7!, t=Times@@(2n+Range[0, 5])}, Table[Floor[t/c], {n, 30}]] (* Harvey P. Dale, Apr 20 2014 *)

Prog

[Floor((2*n)*(2*n+1)*(2*n+2)*(2*n+3)*(2*n+4)*(2*n+5)/Factorial(7)): n in [1..30]]; // Vincenzo Librandi, Apr 10 2012
(Haskell)
a000972 n = a258708 n (n - 7)  -- Reinhard Zumkeller, Jun 23 2015
(PARI) Vec(x^7*(1 + 6*x + 9*x^2 + 9*x^3 + 10*x^4 + 7*x^5 + 12*x^6 + 6*x^7 + 4*x^8) / ((1 - x)^7*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^50)) \\ Colin Barker, Mar 28 2017

Crossrefs

Cf. A258708.

Sequence in context: A112142 A271870 A114243 * A180392 A161805 A036399

Adjacent sequences: A000969 A000970 A000971 * A000973 A000974 A000975

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved