cp's OEIS Frontend

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

%I A027477 #8 Jan 20 2019 07:54:26
%S A027477 1,3,1,23,12,1,330,215,30,1,7604,5700,1035,60,1,256620,212464,45675,
%T A027477 3535,105,1,11923260,10645152,2582209,241080,9730,168,1,729524880,
%U A027477 691560092,183962268,19661649,970200,23058,252,1
%N A027477 Triangle of the square of the normalized, unsigned Stirling matrix of the first kind.
%F A027477 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 A027477 T is the lower triangular matrix  A.A.N.
%e A027477 First rows of the triangle are:
%e A027477 1,
%e A027477 3,1,
%e A027477 23,12,1,
%e A027477 330,215,30,1,
%e A027477 7604,5700,1035,60,1,
%e A027477 256620,212464,45675,3535,105,1
%e A027477 ...
%t A027477 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 A027477 Cf. A027478, A027479 (third and fourth power).
%K A027477 nonn,tabl,easy
%O A027477 1,2
%A A027477 _Olivier Gérard_
%E A027477 Definition, formula and program edited for clarity by _Olivier Gérard_, Jan 20 2019