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%I #21 Oct 18 2018 10:54:57
%S 10,90,720,5040,30240,151200,604800,1814400,3628800,3628800,3628820,
%T 3629180,3635640,3745080,5489280,31536000,394329600,5082739200,
%U 60952953600,670446201600,670446201630,670446202470,670446225960,670446859320,670463302320,670873719600
%N a(n) = 10*9*8*7*6*5*4*3*2*1 + 20*19*18*17*16*15*14*13*12*11 + ... + (up to the n-th term).
%C 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=10.
%H Colin Barker, <a href="/A319874/b319874.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1) = 10;
%e a(2) = 10*9 = 90;
%e a(3) = 10*9*8 = 720;
%e a(4) = 10*9*8*7 = 5040;
%e a(5) = 10*9*8*7*6 = 30240;
%e a(6) = 10*9*8*7*6*5 = 151200;
%e a(7) = 10*9*8*7*6*5*4 = 604800;
%e a(8) = 10*9*8*7*6*5*4*3 = 1814400;
%e a(9) = 10*9*8*7*6*5*4*3*2 = 3628800;
%e a(10) = 10*9*8*7*6*5*4*3*2*1 = 3628800;
%e a(11) = 10*9*8*7*6*5*4*3*2*1 + 20 = 3628820;
%e a(12) = 10*9*8*7*6*5*4*3*2*1 + 20*19 = 3629180;
%e a(13) = 10*9*8*7*6*5*4*3*2*1 + 20*19*18 = 3635640;
%e a(14) = 10*9*8*7*6*5*4*3*2*1 + 20*19*18*17 = 3745080;
%e a(15) = 10*9*8*7*6*5*4*3*2*1 + 20*19*18*17*16 = 5489280;
%e a(16) = 10*9*8*7*6*5*4*3*2*1 + 20*19*18*17*16*15 = 31536000;
%e a(17) = 10*9*8*7*6*5*4*3*2*1 + 20*19*18*17*16*15*14 = 394329600;
%e a(18) = 10*9*8*7*6*5*4*3*2*1 + 20*19*18*17*16*15*14*13 = 5082739200;
%e a(19) = 10*9*8*7*6*5*4*3*2*1 + 20*19*18*17*16*15*14*13*12 = 60952953600;
%e etc.
%p 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,10),n=1..25); # _Muniru A Asiru_, Sep 30 2018
%t k:=10; 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 For similar sequences, see: A000217 (k=1), A319866 (k=2), A319867 (k=3), A319868 (k=4), A319869 (k=5), A319870 (k=6), A319871 (k=7), A319872 (k=8), A319873 (k=9), this sequence (k=10).
%K nonn,easy
%O 1,1
%A _Wesley Ivan Hurt_, Sep 30 2018
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