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

1,2

Links

Table of n, a(n) for n=1..36.

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.

Example

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
...

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]]

Crossrefs

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

Sequence in context: A370948 A306619 A335644 * A260780 A243769 A137330

Adjacent sequences: A027474 A027475 A027476 * A027478 A027479 A027480

Keyword

nonn,tabl,easy

Author

Olivier Gérard

Extensions

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

Status

approved