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A039816
Triangle read by rows: matrix 4th power of the Stirling-1 triangle A008275.
7
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
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.
Sequence in context: A136234 A196528 A135897 * A329060 A118283 A095891
KEYWORD
sign,tabl
AUTHOR
Christian G. Bower, Feb 15 1999
STATUS
approved