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 A178048 #15 Feb 09 2025 02:44:46
%S A178048 1,1,1,1,8,1,1,68,68,1,1,374,2340,374,1,1,1742,47012,47012,1742,1,1,
%T A178048 7524,717948,2942288,717948,7524,1,1,31320,9259560,122248688,
%U A178048 122248688,9259560,31320,1,1,127946,106900560,3895086794,12203119800,3895086794,106900560,127946,1
%N A178048 Triangle T(n, m) = ( |-A008292(n+1,m+1)^2 + 2*binomial(n, m)^2| + A008292(n+1,m+1)*binomial(n, m) )/2 read by rows.
%F A178048 T(n, m) = T(n,n-m).
%e A178048 The triangle starts in row n=0 with columns 0 <= m <= n as
%e A178048 1;
%e A178048 1, 1;
%e A178048 1, 8, 1;
%e A178048 1, 68, 68, 1;
%e A178048 1, 374, 2340, 374, 1;
%e A178048 1, 1742, 47012, 47012, 1742, 1;
%e A178048 1, 7524, 717948, 2942288, 717948, 7524, 1;
%e A178048 1, 31320, 9259560, 122248688, 122248688, 9259560, 31320, 1;
%e A178048 1, 127946, 106900560, 3895086794, 12203119800, 3895086794, 106900560, 127946, 1;
%p A178048 A178048 := proc(n,m) binomial(n,m)*A008292(n+1,m+1)+abs( -A008292(n+1,m+1)^2+2*binomial(n,m)^2) ; %/2; end proc:
%p A178048 seq(seq(A178048(n,k),k=0..n),n=0..10) ; # _R. J. Mathar_, Nov 26 2010
%t A178048 << DiscreteMath`Combinatorica`
%t A178048 t[n_, m_] = (Abs[2*Binomial[n, m]^2 - Eulerian[n + 1, m]^2] + Binomial[n, m]*Eulerian[n + 1, m])/2;
%t A178048 Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t A178048 Flatten[%]
%Y A178048 Cf. A141686, A008292.
%K A178048 nonn,tabl
%O A178048 0,5
%A A178048 _Roger L. Bagula_, May 18 2010
%E A178048 Definition corrected by _R. J. Mathar_, Nov 26 2010