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A039813 Matrix 5th power of Stirling2 triangle A008277.

%I A039813 #31 Feb 13 2022 06:31:29
%S A039813 1,5,1,35,15,1,315,215,30,1,3455,3325,725,50,1,44590,56605,17100,1825,
%T A039813 75,1,660665,1060780,415555,60900,3850,105,1,11035095,21772595,
%U A039813 10606470,1998605,172550,7210,140,1,204904830,486459105,286281665,66528210,7346955,417690,12390,180,1
%N A039813 Matrix 5th power of Stirling2 triangle A008277.
%H A039813 Seiichi Manyama, <a href="/A039813/b039813.txt">Rows n = 1..140, flattened</a>
%F A039813 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 A039813 Triangle begins:
%e A039813       1;
%e A039813       5,     1;
%e A039813      35,    15,     1;
%e A039813     315,   215,    30,    1;
%e A039813    3455,  3325,   725,   50,  1;
%e A039813   44590, 56605, 17100, 1825, 75, 1;
%e A039813   ...
%t A039813 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 A039813 Cf. A008277, A000357 (first column).
%Y A039813 Cf. A039810, A039811, A039812.
%K A039813 nonn,tabl
%O A039813 1,2
%A A039813 _Christian G. Bower_, Feb 15 1999