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 A078921 #19 Jun 29 2025 03:34:16
%S A078921 1,-1,2,2,-3,6,-6,8,-12,24,24,-30,40,-60,120,-120,144,-180,240,-360,
%T A078921 720,720,-840,1008,-1260,1680,-2520,5040,-5040,5760,-6720,8064,-10080,
%U A078921 13440,-20160,40320,40320,-45360,51840,-60480,72576,-90720,120960,-181440,362880,-362880,403200,-453600,518400,-604800,725760,-907200,1209600,-1814400,3628800
%N A078921 Signed variant of A077012.
%C A078921 Row sums give A024167.
%F A078921 T(n, k) = -(-1)^(n-k+1)*(n/(n-k+1))*(n-1)!.
%F A078921 E.g.f.: log(1+x)/(1-y*x). - _Vladeta Jovovic_, Feb 07 2003
%F A078921 Sum_{n>=1} Sum_{k=1..n} 1/T(n, k) = (e^2+1)/(4*e). - _Amiram Eldar_, Jun 29 2025
%e A078921 Triangle starts:
%e A078921 1
%e A078921 -1, 2
%e A078921 2, -3, 6
%e A078921 -6, 8, -12, 24
%e A078921 24, -30, 40, -60, 120
%e A078921 -120, 144, -180, 240, -360, 720
%e A078921 720, -840, 1008, -1260, 1680, -2520, 5040
%e A078921 ...
%t A078921 Table[Table[ -(-1)^(n-k+1) n/(n-k+1), {k, 1, n}] (n-1)!, {n, 1, 12}]
%Y A078921 Cf. A000254, A024167, A077012, A078922.
%K A078921 easy,sign,tabl
%O A078921 1,3
%A A078921 _Wouter Meeussen_, Dec 14 2002