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A090683
Triangle read by rows, defined by T(n,k) = C(n,k)*S2(n,k), 0 <= k <= n, where C(n,k) are the binomial coefficients and S2(n,k) are the Stirling numbers of the second kind.
3
1, 0, 1, 0, 2, 1, 0, 3, 9, 1, 0, 4, 42, 24, 1, 0, 5, 150, 250, 50, 1, 0, 6, 465, 1800, 975, 90, 1, 0, 7, 1323, 10535, 12250, 2940, 147, 1, 0, 8, 3556, 54096, 119070, 58800, 7448, 224, 1, 0, 9, 9180, 254100, 979020, 875826, 222264, 16632, 324, 1, 0, 10, 22995, 1119600, 7162050, 10716300, 4793670, 705600, 33750, 450, 1
OFFSET
0,5
COMMENTS
T(n,k) is the number of Green's H-classes contained in the D-class of rank k in the full transformation semigroup on [n]. - Geoffrey Critzer, Dec 27 2022
REFERENCES
O. Ganyushkin and V. Mazorchuk, Classical Finite Transformation Semigroups, Springer, 2009, pages 58-62.
LINKS
FORMULA
T(n, k) = binomial(n,k)*Stirling2(n,k).
T(n, k) = A007318(n, k)*A048993(n, k).
T(n, k) = A090657(n, k)/k!.
EXAMPLE
Triangle begins:
1;
0, 1;
0, 2, 1;
0, 3, 9, 1;
0, 4, 42, 24, 1;
...
MATHEMATICA
Flatten[Table[Table[Binomial[n, k] StirlingS2[n, k], {k, 0, n}], {n, 0, 10}], 1]
PROG
(Maxima) create_list(binomial(n, k)*stirling2(n, k), n, 0, 12, k, 0, n); /* Emanuele Munarini, Mar 11 2011 */
CROSSREFS
Row sum sequence is A122455.
Sequence in context: A357103 A278882 A153007 * A356263 A320825 A161552
KEYWORD
easy,nonn,tabl
AUTHOR
Philippe Deléham, Dec 18 2003
EXTENSIONS
Edited by Olivier Gérard, Oct 23 2012
STATUS
approved