A000972 Fermat coefficients.

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A258708.

Programs

Haskell

a000972 n = a258708 n (n - 7)  -- Reinhard Zumkeller, Jun 23 2015

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 *)

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

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