A039811 Triangle read by rows: matrix cube of the Stirling2 triangle A008277.

1, 3, 1, 12, 9, 1, 60, 75, 18, 1, 358, 660, 255, 30, 1, 2471, 6288, 3465, 645, 45, 1, 19302, 65051, 47838, 12495, 1365, 63, 1, 167894, 728556, 685580, 235193, 35700, 2562, 84, 1, 1606137, 8792910, 10285488, 4444188, 877653, 86940, 4410, 108, 1

Offset

1,2

Links

Seiichi Manyama, Rows n = 1..140, flattened

Peter Bala, Generalized Dobinski formulas.

Formula

E.g.f. k-th column: (( exp(exp(exp(x)-1)-1)-1 )^k)/k!. [corrected by Seiichi Manyama, Feb 12 2022]

Dobinski-type formula for the n-th row polnomial: R(n, x) = exp(-x) * Sum_{k >= 0} P(n, k)*x^k/k!, where P(n, x) denotes the n-th row polynomial of A039810. - Peter Bala, Nov 07 2025

Example

Triangle begins
     1;
     3,    1;
    12,    9,    1;
    60,   75,   18,   1;
   358,  660,  255,  30,  1;
  2471, 6288, 3465, 645, 45, 1;
  ...

Mathematica

Flatten[Table[SeriesCoefficient[(Exp[Exp[Exp[x]-1]-1]-1)^k, {x, 0, n}] n!/k!, {n, 9}, {k, n}]] (* Stefano Spezia, Sep 12 2022 *)

Crossrefs

Cf. A008277, A000258 (first column).

Cf. also A039810, A039812, A039813.

Sequence in context: A156366 A144353 A356146 * A046089 A113360 A089434

Adjacent sequences: A039808 A039809 A039810 * A039812 A039813 A039814

Keyword

nonn,tabl

Author

Christian G. Bower, Feb 15 1999

Status

approved