|
%I #32 Apr 12 2023 08:06:50
%S 1,7,28,84,210,462,924,1717,3017,5110,8568,14756,27132,54264,116281,
%T 257775,572264,1246784,2641366,5430530,10861060,21242341,40927033,
%U 78354346,150402700,291693136,574274008,1148548016,2326683921,4749439975,9714753412,19818498700,40199107690
%N Expansion of 1/((1-x)^7 - x^7).
%C Differs for n >= 7 (1717 vs. 1716) from A000579(n+6) = binomial(n+6,6); see also row 6 of A027555, A059481 and A213808. - _M. F. Hasler_, Mar 05 2017
%H Seiichi Manyama, <a href="/A049017/b049017.txt">Table of n, a(n) for n = 0..3000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,2).
%F G.f.: 1/((1-x)^7 - x^7) = 1/((1-2*x)*(1-5*x+11*x^2-13*x^3+9*x^4-3*x^5+x^6)).
%t CoefficientList[Series[1/((1-x)^7-x^7),{x,0,30}],x] (* _Harvey P. Dale_, Feb 18 2011 *)
%o (PARI) Vec(1/((1-x)^7-x^7)+O(x^99)) \\ _M. F. Hasler_, Mar 05 2017
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1-x)^7 - x^7) )); // _G. C. Greubel_, Apr 11 2023
%o (SageMath)
%o def A049017_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 1/((1-x)^7 - x^7) ).list()
%o A049017_list(40) # _G. C. Greubel_, Apr 11 2023
%Y Cf. A000579, A000750, A027555, A049018, A059481, A213808.
%Y Sequences of the form 1/((1-x)^m - x^m): A000079 (m=1,2), A024495 (m=3), A000749 (m=4), A049016 (m=5), A192080 (m=6), this sequence (m=7), A290995 (m=8), A306939 (m=9).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
|
