A039816 Triangle read by rows: matrix 4th power of the Stirling-1 triangle A008275.

1, -4, 1, 26, -12, 1, -234, 152, -24, 1, 2696, -2210, 500, -40, 1, -37919, 36976, -10710, 1240, -60, 1, 630521, -704837, 245896, -36750, 2590, -84, 1, -12111114, 15132932, -6120324, 1109696, -101500, 4816, -112, 1, 264051201, -362099010, 165387680, -34990620, 3901296, -241164, 8232, -144, 1

Offset: 1

Author

Christian G. Bower, Feb 15 1999

Keywords

• sign
• tabl

Examples

			Triangle begins:
       1;
      -4,     1;
      26,   -12,      1;
    -234,   152,    -24,    1;
    2696, -2210,    500,  -40,   1;
  -37919, 36976, -10710, 1240, -60, 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. A000310 (first column), A008275.

Cf. A039812, A039814, A039815, A039817.

Programs

Maple

T:= Matrix(10,10,(i,j) -> `if`(i>= j, combinat:-stirling1(i,j),0)):
M:= T^4:
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+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+log(1+x)))))^k)/k!.