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A027477 Triangle of the square of the normalized, unsigned Stirling matrix of the first kind. 6

%I

%S 1,3,1,23,12,1,330,215,30,1,7604,5700,1035,60,1,256620,212464,45675,

%T 3535,105,1,11923260,10645152,2582209,241080,9730,168,1,729524880,

%U 691560092,183962268,19661649,970200,23058,252,1

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

%F 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)).

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

%e First rows of the triangle are:

%e 1,

%e 3,1,

%e 23,12,1,

%e 330,215,30,1,

%e 7604,5700,1035,60,1,

%e 256620,212464,45675,3535,105,1

%e ...

%t 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]]

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

%K nonn,tabl,easy

%O 1,2

%A _Olivier Gérard_

%E Definition, formula and program edited for clarity by _Olivier Gérard_, Jan 20 2019

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Last modified January 28 17:14 EST 2022. Contains 350657 sequences. (Running on oeis4.)