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 A157180 #2 Oct 12 2012 14:54:56
%S A157180 1,1,1,1,4,1,1,13,13,1,1,34,78,34,1,1,79,380,380,79,1,1,172,1607,3040,
%T A157180 1607,172,1,1,361,6135,20383,20383,6135,361,1,1,742,21796,120826,
%U A157180 203830,120826,21796,742,1,1,1507,73654,652994,1751524,1751524,652994,73654
%N A157180 A new general triangle sequence based on the Eulerian form in three parts ( subtraction):m=2; t0(n,k)=If[n*k == 0, 1, Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]] t(n,k,m)=If[n == 0, 1, ( m*(n - k) + 1)*t0(n - 1 + 1, k - 1) + (m*k + 1)*t0(n - 1 + 1, k) - m*k*(n - k)*t0(n - 2 + 1, k - 1)].
%C A157180 Row sums are:
%C A157180 {1, 2, 6, 28, 148, 920, 6600, 53760, 490560, 4959360, 55036800,...}.
%C A157180 The m=0 of the general sequence is A008518.
%F A157180 m=2;
%F A157180 t0(n,k)=If[n*k == 0, 1, Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]];
%F A157180 t(n,k,m)=If[n == 0, 1, ( m*(n - k) + 1)*t0(n - 1 + 1, k - 1) +
%F A157180 (m*k + 1)*t0(n - 1 + 1, k) +
%F A157180 m*k*(n - k)*t0(n - 2 + 1, k - 1)].
%e A157180 {1},
%e A157180 {1, 1},
%e A157180 {1, 4, 1},
%e A157180 {1, 13, 13, 1},
%e A157180 {1, 34, 78, 34, 1},
%e A157180 {1, 79, 380, 380, 79, 1},
%e A157180 {1, 172, 1607, 3040, 1607, 172, 1},
%e A157180 {1, 361, 6135, 20383, 20383, 6135, 361, 1},
%e A157180 {1, 742, 21796, 120826, 203830, 120826, 21796, 742, 1},
%e A157180 {1, 1507, 73654, 652994, 1751524, 1751524, 652994, 73654, 1507, 1},
%e A157180 {1, 3040, 240357, 3290408, 13475450, 21018288, 13475450, 3290408, 240357, 3040, 1}
%t A157180 Clear[t, n, k, m];
%t A157180 t[n_, k_, m_] = (m*(n - k) + 1)*Binomial[n - 1, k - 1] + (m*k + 1)*Binomial[n - 1, k] - m*k*(n - k)*Binomial[n - 2, k - 1];
%t A157180 Table[t[n, k, m], {m, 0, 10}, {n, 0, 10}, {k, 0, n}];
%t A157180 Table[Flatten[Table[Table[t[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}]
%t A157180 Table[Table[Sum[t[n, k, m], {k, 0, n}], {n, 0, 10}], {m, 0, 10}];
%Y A157180 A008518
%K A157180 nonn,tabl
%O A157180 0,5
%A A157180 _Roger L. Bagula_ and _Gary W. Adamson_, Feb 24 2009