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

1, -3, 1, 15, -9, 1, -105, 87, -18, 1, 947, -975, 285, -30, 1, -10472, 12657, -4680, 705, -45, 1, 137337, -188090, 82887, -15960, 1470, -63, 1, -2085605, 3159699, -1598954, 370237, -43890, 2730, -84, 1, 36017472, -59326371, 33613353, -9009294, 1292067, -103950, 4662, -108, 1

Offset: 1

Author

Christian G. Bower, Feb 15 1999

Keywords

• sign
• tabl

Examples

			Triangle begins:
       1;
      -3,     1;
      15,    -9,     1;
    -105,    87,   -18,   1;
     947,  -975,   285, -30,   1;
  -10472, 12657, -4680, 705, -45, 1;
  ...
		

Links

• Seiichi Manyama, Rows n = 1..140, flattened
• Gabriella Bretti, Pierpaolo Natalini and Paolo E. Ricci, A new set of Sheffer-Bell polynomials and logarithmic numbers, Georgian Mathematical Journal, Feb. 2019, page 9.

Crossrefs

Cf. A000268 (first column), A008275.

Cf. A039811, A039814, A039816, A039817.

Programs

Maple

T:= Matrix(10,10,(i,j) -> `if`(i>= j, combinat:-stirling1(i,j),0)):
M:= T^3:
seq(seq(M[i,j],j=1..i),i=1..10); # Robert Israel, Sep 12 2022

Mathematica

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 *)

Formula

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