A027479 Triangle of the fourth power of the normalized, unsigned Stirling matrix of the first kind.

1, 15, 1, 1175, 120, 1, 294330, 36935, 510, 1, 181082204, 25816200, 460035, 1560, 1, 231844265940, 36133755364, 757122975, 3411835, 3885, 1, 551220029003580, 91850446178400, 2159098539409, 11690792400, 18037810, 8400, 1, 2239429013789400720, 393327895035809180, 10088942720014620, 62324463343569, 117282133080, 75042450, 16380, 1

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• tabl
• easy

Examples

			First rows of the triangle are:
          1;
         15,        1;
       1175,      120,      1;
     294330,    36935,    510,    1;
  181082204, 25816200, 460035, 1560, 1;
  ...
		

Crossrefs

Cf. A027477 (second-order triangle), A027478 (third-order triangle).

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.m.m*Table[i!^4,{i,1,nmax}]; Flatten[Table[Table[m[[i,j]],{j,1,i}],{i,1,nmax}],1]]

Extensions

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