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A027477 Triangle of the square of the normalized, unsigned Stirling matrix of the first kind. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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: A010291 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

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Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)