A027477 Triangle of the square of the normalized, unsigned Stirling matrix of the first kind.

1, 3, 1, 23, 12, 1, 330, 215, 30, 1, 7604, 5700, 1035, 60, 1, 256620, 212464, 45675, 3535, 105, 1, 11923260, 10645152, 2582209, 241080, 9730, 168, 1, 729524880, 691560092, 183962268, 19661649, 970200, 23058, 252, 1

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• tabl
• easy

Examples

			First rows of the triangle are:
1,
3,1,
23,12,1,
330,215,30,1,
7604,5700,1035,60,1,
256620,212464,45675,3535,105,1
...
		

Crossrefs

Cf. A027478, A027479 (third and fourth power).

Programs

Mathematica

Module[{nmax=8,m},m=(Table[Table[(-1)^(i+j) StirlingS1[i,j]/i!,{j,1,nmax}],{i,1,nmax}]);m=m.m*Table[i!^2,{i,1,nmax}]; Flatten[Table[Table[m[[i,j]],{j,1,i}],{i,1,nmax}],1]]

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!^2)).

T is the lower triangular matrix A.A.N.

Extensions

Definition, formula and program edited for clarity by Olivier Gérard, Jan 20 2019