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A039815 Triangle read by rows: matrix cube of the Stirling-1 triangle A008275.

%I A039815 #30 Sep 18 2022 12:36:33
%S A039815 1,-3,1,15,-9,1,-105,87,-18,1,947,-975,285,-30,1,-10472,12657,-4680,
%T A039815 705,-45,1,137337,-188090,82887,-15960,1470,-63,1,-2085605,3159699,
%U A039815 -1598954,370237,-43890,2730,-84,1,36017472,-59326371,33613353,-9009294,1292067,-103950,4662,-108,1
%N A039815 Triangle read by rows: matrix cube of the Stirling-1 triangle A008275.
%H A039815 Seiichi Manyama, <a href="/A039815/b039815.txt">Rows n = 1..140, flattened</a>
%H A039815 Gabriella Bretti, Pierpaolo Natalini and Paolo E. Ricci, <a href="https://doi.org/10.1515/gmj-2019-2007">A new set of Sheffer-Bell polynomials and logarithmic numbers</a>, Georgian Mathematical Journal, Feb. 2019, page 9.
%F A039815 E.g.f. of k-th column: ((log(1+log(1+log(1+x))))^k)/k!.
%e A039815 Triangle begins:
%e A039815        1;
%e A039815       -3,     1;
%e A039815       15,    -9,     1;
%e A039815     -105,    87,   -18,   1;
%e A039815      947,  -975,   285, -30,   1;
%e A039815   -10472, 12657, -4680, 705, -45, 1;
%e A039815   ...
%p A039815 T:= Matrix(10,10,(i,j) -> `if`(i>= j, combinat:-stirling1(i,j),0)):
%p A039815 M:= T^3:
%p A039815 seq(seq(M[i,j],j=1..i),i=1..10); # _Robert Israel_, Sep 12 2022
%t A039815 Flatten[Table[SeriesCoefficient[(Log[1+Log[1+Log[1+x]]])^k, {x,0,n}] n!/k!, {n,9}, {k,n}]] (* _Stefano Spezia_, Sep 12 2022 *)
%Y A039815 Cf. A000268 (first column), A008275.
%Y A039815 Cf. A039811, A039814, A039816, A039817.
%K A039815 sign,tabl
%O A039815 1,2
%A A039815 _Christian G. Bower_, Feb 15 1999