cp's OEIS Frontend

A116690 a(n) = C(n,8) + C(n,7) + C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).

%I A116690 #25 Aug 14 2023 11:24:17
%S A116690 0,1,3,7,15,31,63,127,255,510,1012,1980,3796,7098,12910,22818,39202,
%T A116690 65535,106761,169765,263949,401929,600369,880969,1271625,1807780,
%U A116690 2533986,3505698,4791322,6474540,8656936,11460948,15033172,19548045
%N A116690 a(n) = C(n,8) + C(n,7) + C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).
%H A116690 G. C. Greubel, <a href="/A116690/b116690.txt">Table of n, a(n) for n = 0..1000</a>
%H A116690 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A116690 a(n) = A000581(n) + A000580(n) + A000579(n) + A000389(n) + A000332(n) + A000292(n) + A000217(n) + n. a(n) = A000581(n) + A116082(n).
%F A116690 G.f. ( -x*(2*x^2 - 2*x + 1)*(2*x^4 - 4*x^3 + 6*x^2 - 4*x + 1) ) / (x-1)^9. - _R. J. Mathar_, Oct 21 2011
%F A116690 a(n) = n*(n+1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6)/40320. - _G. C. Greubel_, Nov 25 2017
%p A116690 seq(sum(binomial(n,k),k=1..8),n=0..33); # _Zerinvary Lajos_, Dec 14 2007
%t A116690 Table[n*(n + 1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6)/40320, {n, 0, 50}] (* _G. C. Greubel_, Nov 25 2017 *)
%t A116690 Table[Total[Binomial[n,Range[8]]],{n,0,40}] (* _Harvey P. Dale_, Aug 14 2023 *)
%o A116690 (Sage) [binomial(n,2)+binomial(n,4)+binomial(n,6)+binomial(n,8) for n in range(1, 35)] # _Zerinvary Lajos_, May 17 2009
%o A116690 (Sage) [binomial(n,2)+binomial(n,4)+binomial(n,6)+binomial(n,8)+binomial(n,1)+binomial(n,3)+binomial(n,5)+binomial(n,7)for n in range(0, 34)] # _Zerinvary Lajos_, May 17 2009
%o A116690 (PARI) for(n=0,30, print1(n*(n+1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6 ) /40320, ", ")) \\ _G. C. Greubel_, Nov 25 2017
%o A116690 (Magma) [n*(n+1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6 ) /40320: n in [0..30]]; // _G. C. Greubel_, Nov 25 2017
%K A116690 easy,nonn
%O A116690 0,3
%A A116690 _Jonathan Vos Post_, Mar 15 2006