A039813 - OEIS

%I #31 Feb 13 2022 06:31:29

%S 1,5,1,35,15,1,315,215,30,1,3455,3325,725,50,1,44590,56605,17100,1825,

%T 75,1,660665,1060780,415555,60900,3850,105,1,11035095,21772595,

%U 10606470,1998605,172550,7210,140,1,204904830,486459105,286281665,66528210,7346955,417690,12390,180,1

%N Matrix 5th power of Stirling2 triangle A008277.

%H Seiichi Manyama, <a href="/A039813/b039813.txt">Rows n = 1..140, flattened</a>

%F 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]

%e Triangle begins:

%e       1;

%e       5,     1;

%e      35,    15,     1;

%e     315,   215,    30,    1;

%e    3455,  3325,   725,   50,  1;

%e   44590, 56605, 17100, 1825, 75, 1;

%e   ...

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

%Y Cf. A008277, A000357 (first column).

%Y Cf. A039810, A039811, A039812.

%K nonn,tabl

%O 1,2

%A _Christian G. Bower_, Feb 15 1999