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

1,2

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.

Formula

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

Example

Triangle begins:
       1;
      -4,     1;
      26,   -12,      1;
    -234,   152,    -24,    1;
    2696, -2210,    500,  -40,   1;
  -37919, 36976, -10710, 1240, -60, 1;
  ...

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 *)

Crossrefs

Cf. A000310 (first column), A008275.

Cf. A039812, A039814, A039815, A039817.

Sequence in context: A136234 A196528 A135897 * A329060 A118283 A095891

Adjacent sequences: A039813 A039814 A039815 * A039817 A039818 A039819

Keyword

sign,tabl

Author

Christian G. Bower, Feb 15 1999

Status

approved