cp's OEIS Frontend

A319871 a(n) = 7*6*5*4*3*2*1 + 14*13*12*11*10*9*8 + ... + (up to the n-th term).

%I A319871 #19 Oct 18 2018 10:34:40
%S A319871 7,42,210,840,2520,5040,5040,5054,5222,7224,29064,245280,2167200,
%T A319871 17302320,17302341,17302740,17310300,17445960,19744200,56372400,
%U A319871 603353520,603353548,603354276,603373176,603844920,615147120,874606320,6570915120,6570915155,6570916310
%N A319871 a(n) = 7*6*5*4*3*2*1 + 14*13*12*11*10*9*8 + ... + (up to the n-th term).
%C A319871 For similar multiply/add sequences in descending blocks of k natural numbers, we have: a(n) = Sum_{j=1..k-1} (floor((n-j)/k)-floor((n-j-1)/k)) * (Product_{i=1..j} n-i-j+k+1) + Sum_{j=1..n} (floor(j/k)-floor((j-1)/k)) * (Product_{i=1..k} j-i+1). Here, k=7.
%H A319871 Colin Barker, <a href="/A319871/b319871.txt">Table of n, a(n) for n = 1..1000</a>
%e A319871 a(1) = 7;
%e A319871 a(2) = 7*6 = 42;
%e A319871 a(3) = 7*6*5 = 210;
%e A319871 a(4) = 7*6*5*4 = 840;
%e A319871 a(5) = 7*6*5*4*3 = 2520;
%e A319871 a(6) = 7*6*5*4*3*2 = 5040;
%e A319871 a(7) = 7*6*5*4*3*2*1 = 5040;
%e A319871 a(8) = 7*6*5*4*3*2*1 + 14 = 5054;
%e A319871 a(9) = 7*6*5*4*3*2*1 + 14*13 = 5222;
%e A319871 a(10) = 7*6*5*4*3*2*1 + 14*13*12 = 7224;
%e A319871 a(11) = 7*6*5*4*3*2*1 + 14*13*12*11 = 29064;
%e A319871 a(12) = 7*6*5*4*3*2*1 + 14*13*12*11*10 = 245280;
%e A319871 a(13) = 7*6*5*4*3*2*1 + 14*13*12*11*10*9 = 2167200;
%e A319871 a(14) = 7*6*5*4*3*2*1 + 14*13*12*11*10*9*8 = 17302320;
%e A319871 a(15) = 7*6*5*4*3*2*1 + 14*13*12*11*10*9*8 + 21 = 17302341;
%e A319871 a(16) = 7*6*5*4*3*2*1 + 14*13*12*11*10*9*8 + 21*20 = 17302740;
%e A319871 a(17) = 7*6*5*4*3*2*1 + 14*13*12*11*10*9*8 + 21*20*19 = 17310300;
%e A319871 a(18) = 7*6*5*4*3*2*1 + 14*13*12*11*10*9*8 + 21*20*19*18 = 17445960;
%e A319871 a(19) = 7*6*5*4*3*2*1 + 14*13*12*11*10*9*8 + 21*20*19*18*17 = 19744200;
%e A319871 a(20) = 7*6*5*4*3*2*1 + 14*13*12*11*10*9*8 + 21*20*19*18*17*16 = 56372400;
%e A319871 etc.
%p A319871 a:=(n,k)->add((floor((n-j)/k)-floor((n-j-1)/k))*(mul(n-i-j+k+1,i=1..j)),j=1..k-1) + add((floor(j/k)-floor((j-1)/k))*(mul(j-i+1,i=1..k)),j=1..n): seq(a(n,7),n=1..30); # _Muniru A Asiru_, Sep 30 2018
%t A319871 k:=7; a[n_]:=Sum[(Floor[(n-j)/k]-Floor[(n-j-1)/k])*Product[n-i-j+k+1, {i,1,j }] , {j,1,k-1} ] + Sum[(Floor[j/k]-Floor[(j-1)/k])*Product[j-i+1, {i,1,k}], {j,1,n}]; Array[a, 50] (* _Stefano Spezia_, Sep 30 2018 *)
%Y A319871 For similar sequences, see: A000217 (k=1), A319866 (k=2), A319867 (k=3), A319868 (k=4), A319869 (k=5), A319870 (k=6), this sequence (k=7), A319872 (k=8), A319873 (k=9), A319874 (k=10).
%K A319871 nonn,easy
%O A319871 1,1
%A A319871 _Wesley Ivan Hurt_, Sep 30 2018