A039815 - OEIS

%I #30 Sep 18 2022 12:36:33

%S 1,-3,1,15,-9,1,-105,87,-18,1,947,-975,285,-30,1,-10472,12657,-4680,

%T 705,-45,1,137337,-188090,82887,-15960,1470,-63,1,-2085605,3159699,

%U -1598954,370237,-43890,2730,-84,1,36017472,-59326371,33613353,-9009294,1292067,-103950,4662,-108,1

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

%H Seiichi Manyama, <a href="/A039815/b039815.txt">Rows n = 1..140, flattened</a>

%H 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 E.g.f. of k-th column: ((log(1+log(1+log(1+x))))^k)/k!.

%e Triangle begins:

%e        1;

%e       -3,     1;

%e       15,    -9,     1;

%e     -105,    87,   -18,   1;

%e      947,  -975,   285, -30,   1;

%e   -10472, 12657, -4680, 705, -45, 1;

%e   ...

%p T:= Matrix(10,10,(i,j) -> `if`(i>= j, combinat:-stirling1(i,j),0)):

%p M:= T^3:

%p seq(seq(M[i,j],j=1..i),i=1..10); # _Robert Israel_, Sep 12 2022

%t 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 Cf. A000268 (first column), A008275.

%Y Cf. A039811, A039814, A039816, A039817.

%K sign,tabl

%O 1,2

%A _Christian G. Bower_, Feb 15 1999