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

1,2

Links

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

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]

Example

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

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 *)

Crossrefs

Cf. A008277, A000357 (first column).

Cf. A039810, A039811, A039812.

Sequence in context: A336599 A066833 A334887 * A160632 A089515 A158820

Adjacent sequences: A039810 A039811 A039812 * A039814 A039815 A039816

Keyword

nonn,tabl

Author

Christian G. Bower, Feb 15 1999

Status

approved