cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A104728 Triangle T(n,k) = (k-1-n)*(k-2-n)*(k-2+2*n)/2 read by rows, 1<=k<=n.

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%I A104728 #12 Dec 25 2018 13:10:05
%S A104728 1,9,4,30,18,7,70,48,27,10,135,100,66,36,13,231,180,130,84,45,16,364,
%T A104728 294,225,160,102,54,19,540,448,357,270,190,120,63,22,765,648,532,420,
%U A104728 315,220,138,72,25,1045,900,756,616,483,360,250,156,81,28,1386,1210,1035,864,700,546,405,280,174,90,31
%N A104728 Triangle T(n,k) = (k-1-n)*(k-2-n)*(k-2+2*n)/2 read by rows, 1<=k<=n.
%C A104728 The triangle is defined as the matrix product A * B, A = [1; 1, 4; 1, 4, 7;...]; B = [1; 2, 1; 3, 2, 1;...]; both infinite lower triangular matrices with the rest of the terms zeros.
%e A104728 The first few rows of the triangle are:
%e A104728 1;
%e A104728 9,    4;
%e A104728 30,   18,   7;
%e A104728 70,   48,   27,   10;
%e A104728 135,  100,  66,   36,   13;
%e A104728 231,  180,  130,  84,   45,  16;
%e A104728 364,  294,  225,  160,  102, 54,  19;
%e A104728 540,  448,  357,  270,  190, 120, 63,  22;
%e A104728 765,  648,  532,  420,  315, 220, 138, 72,  25;
%e A104728 1045, 900,  756,  616,  483, 360, 250, 156, 81,  28;
%e A104728 1386, 1210, 1035, 864,  700, 546, 405, 280, 174, 90,  31;
%e A104728 1794, 1584, 1375, 1170, 972, 784, 609, 450, 310, 192, 99, 34, etc.
%p A104728 A104728 := proc(n)
%p A104728         (k-1-n)*(k-2-n)*(k-2+2*n)/2 ;
%p A104728 end proc:
%p A104728 seq(seq(A104728(n,k),k=1..n),n=1..14) ; # _R. J. Mathar_, Nov 07 2011
%t A104728 Table[(k-1-n)(k-2-n)(k-2+2n)/2,{n,20},{k,n}]//Flatten (* _Harvey P. Dale_, Dec 25 2018 *)
%Y A104728 Cf. A051798 (row sums), A007586, A002414 (column 1).
%K A104728 nonn,easy,tabl
%O A104728 1,2
%A A104728 _Gary W. Adamson_, Mar 20 2005
%E A104728 Name contributed by _R. J. Mathar_, Nov 07 2011