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A039812 Triangle read by rows: matrix 4th power of the Stirling2 triangle A008277.

%I A039812 #32 Sep 18 2022 12:36:29
%S A039812 1,4,1,22,12,1,154,136,24,1,1304,1650,460,40,1,12915,21904,8550,1160,
%T A039812 60,1,146115,318521,162904,30590,2450,84,1,1855570,5051988,3246068,
%U A039812 789824,86940,4592,112,1,26097835,86910426,68151304,20606796,2919504,210924,7896,144,1
%N A039812 Triangle read by rows: matrix 4th power of the Stirling2 triangle A008277.
%H A039812 Seiichi Manyama, <a href="/A039812/b039812.txt">Rows n = 1..140, flattened</a>
%F A039812 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 A039812 Triangle begins
%e A039812       1;
%e A039812       4,     1;
%e A039812      22,    12,    1;
%e A039812     154,   136,   24,    1;
%e A039812    1304,  1650,  460,   40,  1;
%e A039812   12915, 21904, 8550, 1160, 60, 1;
%e A039812   ...
%t A039812 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 A039812 Cf. A008277, A000307 (first column).
%Y A039812 Cf. A039810, A039811, A039813.
%K A039812 nonn,tabl
%O A039812 1,2
%A A039812 _Christian G. Bower_, Feb 15 1999