OFFSET
1,2
COMMENTS
The absolute values are unchanged if one uses the signed Stirling numbers of the first kind.
FORMULA
Let A be the lower triangular matrix with entries a[ i, j ] = (-1)^(i+j)*s(i, j)/i! if j<=i, 0 if j>i, where s(i,j) is the Stirling number of the first kind. Let N be the column vector ((i!^3)).
T is the lower triangular matrix A.A.A.N.
EXAMPLE
The first rows of the triangle are :
1,
7, 1,
176, 39, 1,
10746, 2951, 126, 1,
1297704, 407450, 22535, 310, 1,
272866980, 94128364, 6139575, 112435, 645, 1,
...
MATHEMATICA
Module[{nmax=8, m}, m=(Table[Table[(-1)^(i+j) StirlingS1[i, j]/i!, {j, 1, nmax}], {i, 1, nmax}]); m=m.m.m*Table[i!^3, {i, 1, nmax}]; Flatten[Table[Table[m[[i, j]], {j, 1, i}], {i, 1, nmax}], 1]]
CROSSREFS
KEYWORD
AUTHOR
EXTENSIONS
Definition, formula and program edited for clarity by Olivier Gérard, Jan 20 2019
STATUS
approved