A039813 Matrix 5th power of Stirling2 triangle A008277.

1, 5, 1, 35, 15, 1, 315, 215, 30, 1, 3455, 3325, 725, 50, 1, 44590, 56605, 17100, 1825, 75, 1, 660665, 1060780, 415555, 60900, 3850, 105, 1, 11035095, 21772595, 10606470, 1998605, 172550, 7210, 140, 1, 204904830, 486459105, 286281665, 66528210, 7346955, 417690, 12390, 180, 1

Offset: 1

Author

Christian G. Bower, Feb 15 1999

Keywords

• nonn
• tabl

Examples

			Triangle begins:
      1;
      5,     1;
     35,    15,     1;
    315,   215,    30,    1;
   3455,  3325,   725,   50,  1;
  44590, 56605, 17100, 1825, 75, 1;
  ...
		

Links

• Seiichi Manyama, Rows n = 1..140, flattened

Crossrefs

Cf. A008277, A000357 (first column).

Cf. A039810, A039811, A039812.

Programs

Mathematica

max = 9; m = MatrixPower[Array[StirlingS2, {max, max}], 5]; Table[Take[m[[n]], n], {n, 1, max}] // Flatten (* Jean-François Alcover, Mar 03 2014 *)

Formula

E.g.f. k-th column: (( exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1 )^k)/k!. [corrected by Seiichi Manyama, Feb 12 2022]