A055326 Column 1 of triangle A055325.
1, -1, 3, -23, 425, -18129, 1721419, -353654167, 153923102577, -139765654884545, 261831303051976691, -1003756293946036677111, 7827579773381983088436313, -123626888505819540001029957073
Offset: 1
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.
Triangle begins:
{1},
{1, 1},
{3, 4, 1},
{23, 33, 11, 1},
{425, 620, 220, 26, 1},
{18129, 26525, 9520, 1180, 57, 1},
{1721419, 2519664, 905765, 113050, 5649, 120, 1},
{353654167, 517670461, 186123259, 23248085, 1166221, 25347, 247, 1},
{153923102577, 225309742552, 81009042744, 10119247684, 507795498, 11059468, 109386, 502, 1},
...
t[n_,k_]:=Sum[(-1)^j Binomial[n,j](k+1-j)^(n-1),{j,0,k}];
M[n_]:=Table[If[k <= m,(-1)^(m+k)*t[m,k],0],{k,0,n-2},{m,2,n}];
Flatten[Table[Table[Inverse[M[12]][[m,n]],{m,1,n}],{n,1,11}]]
{1},
{1, 1},
{5, 6, 1},
{93, 115, 23, 1},
{5993, 7436, 1518, 76, 1},
{1272089, 1578757, 322762, 16330, 237, 1},
{857402029, 1064110290, 217560951, 11012540, 160571, 722, 1},
{1792650585525, 2224835452407, 454875884137, 23025275075, 335768223, 1512581, 2179, 1},
{11464255554367057, 14228139328931096, 2908996087466828, 147249943814184, 2147290464886, 9673492136, 13945196, 6552, 1},
{222406320165016449457, 276025608122908733321, 56434463826320585284, 2856645864675796564, 41657391444153086, 187665608020478, 270538484020, 127141156, 19673, 1},
{13026233415367869864109781, 16166689855580307839632286, 3305339964838291288943901, 167312402773377971746920, 2439853795947184617546, 10991486289326969076, 15845312257310658, 7446608913000, 1152338433, 59038, 1}
m = 2;
A[n_, 1] := 1
A[n_, n_] := 1
A[n_, k_] := (m*n - m*k + 1)A[n - 1, k - 1] + (m*k - (m - 1))A[n - 1, k]
a = Table[A[n, k], {n, 12}, {k, n}]
M[n_] := Table[If[k <= m, (-1)^(m + k)*a[[m, k]], 0], {k, 1, n}, {m, 1, n}]
Table[Table[Inverse[M[12]][[m, n]], {m, 1, n}], {n, 1, 11}]
Flatten[%]