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Triangle read by rows: matrix 4th power of the Stirling2 triangle A008277.
6

%I #32 Sep 18 2022 12:36:29

%S 1,4,1,22,12,1,154,136,24,1,1304,1650,460,40,1,12915,21904,8550,1160,

%T 60,1,146115,318521,162904,30590,2450,84,1,1855570,5051988,3246068,

%U 789824,86940,4592,112,1,26097835,86910426,68151304,20606796,2919504,210924,7896,144,1

%N Triangle read by rows: matrix 4th power of the Stirling2 triangle A008277.

%H Seiichi Manyama, <a href="/A039812/b039812.txt">Rows n = 1..140, flattened</a>

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

%e Triangle begins

%e 1;

%e 4, 1;

%e 22, 12, 1;

%e 154, 136, 24, 1;

%e 1304, 1650, 460, 40, 1;

%e 12915, 21904, 8550, 1160, 60, 1;

%e ...

%t Flatten[Table[SeriesCoefficient[(Exp[Exp[Exp[Exp[x]-1]-1]-1]-1)^k, {x,0,n}] n!/k!, {n,9}, {k,n}]] (* _Stefano Spezia_, Sep 12 2022 *)

%Y Cf. A008277, A000307 (first column).

%Y Cf. A039810, A039811, A039813.

%K nonn,tabl

%O 1,2

%A _Christian G. Bower_, Feb 15 1999