cp's OEIS Frontend

A000972 Fermat coefficients.

%I A000972 M4847 N2072 #30 Mar 28 2017 14:42:38
%S A000972 1,12,66,245,715,1768,3876,7752,14421,25300,42287,67860,105183,158224,
%T A000972 231880,332112,466089,642341,870922,1163580,1533939,1997688,2572780,
%U A000972 3279640,4141382,5184036,6436782,7932196,9706503,11799840,14256528,17125353,20459857
%N A000972 Fermat coefficients.
%D A000972 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000972 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000972 Vincenzo Librandi, <a href="/A000972/b000972.txt">Table of n, a(n) for n = 7..1000</a>
%H A000972 R. P. Loh, A. G. Shannon, A. F. Horadam, <a href="/A000969/a000969.pdf">Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients</a>, Preprint, 1980.
%H A000972 P. A. Piza, <a href="http://www.jstor.org/stable/3029103">Fermat coefficients</a>, Math. Mag., 27 (1954), 141-146.
%H A000972 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1,1,-6,15,-20,15,-6,1).
%F A000972 a(n) = A258708(n,n-7). - _Reinhard Zumkeller_, Jun 23 2015
%F A000972 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
%p A000972 a := n->floor((2*n)*(2*n+1)*(2*n+2)*(2*n+3)*(2*n+4)*(2*n+5)/7!);
%t A000972 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 *)
%t A000972 With[{c=7!,t=Times@@(2n+Range[0,5])},Table[Floor[t/c],{n,30}]] (* _Harvey P. Dale_, Apr 20 2014 *)
%o A000972 [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
%o A000972 (Haskell)
%o A000972 a000972 n = a258708 n (n - 7)  -- _Reinhard Zumkeller_, Jun 23 2015
%o A000972 (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
%Y A000972 Cf. A258708.
%K A000972 nonn,easy
%O A000972 7,2
%A A000972 _N. J. A. Sloane_