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.
%I A108085 #16 May 04 2025 16:09:46
%S A108085 1,2,-1,8,-6,1,64,-56,14,-1,1024,-960,280,-30,1,32768,-31744,9920,
%T A108085 -1240,62,-1,2097152,-2064384,666624,-89280,5208,-126,1,268435456,
%U A108085 -266338304,87392256,-12094464,755904,-21336,254,-1,68719476736,-68451041280,22638755840,-3183575040,205605888,-6217920
%N A108085 Triangle, read by rows, where T(0,0) = 1, T(n,k) = 2^n*T(n-1,k) - T(n-1,k-1).
%C A108085 For n > 0, n-th row sum = Product_{i=1..n} (2^i - 1), i.e., A005329(n).
%C A108085 Triangle T(n,k), 0 <= k <= n, read by rows given by [2, 2, 8, 12, 32, 56, 128, 240, 512, ...] DELTA [-1, 0, -2, 0, -4, 0, -8, 0, -16, 0, -32, 0, ...] = A014236(first zero omitted)DELTA -A077957 where DELTA is the operator defined in A084938. - _Philippe Deléham_, Aug 23 2006
%e A108085 Triangle begins
%e A108085 1;
%e A108085 2, -1;
%e A108085 8, -6, 1;
%e A108085 64, -56, 14, -1;
%e A108085 1024, -960, 280, -30, 1;
%o A108085 (PARI) t(n, k) = {if (k < 0, return (0)); if (n < k, return (0)); if (n == 0, return (1)); return (2^n*t(n-1,k) - t(n-1,k-1));} \\ _Michel Marcus_, Apr 11 2013
%K A108085 sign,tabl
%O A108085 0,2
%A A108085 _Gerald McGarvey_, Jun 05 2005