

A277086


Irregular triangle read by rows: T(n,k) = number of size k subsets of S_n with respect to the symmetries of the square.


0



1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 5, 5, 2, 1, 1, 7, 56, 317, 1524, 5733, 17728, 44767, 94427, 166786, 249624, 316950, 343424, 316950, 249624, 166786, 94427, 44767, 17728, 5733, 1524, 317, 56, 7, 1, 1, 23, 1012, 36125, 1035496, 23878229, 456936220, 7437730463
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OFFSET

0,9


COMMENTS

A permutation, p, can be thought of as a set of points (i, p(i)). In this viewpoint it is natural to consider the symmetries of the square.
T(n,k) is the number of symmetry classes of subsets of size k from S_n.


LINKS

Table of n, a(n) for n=0..46.


FORMULA

T(n,k) = 1/8 * (C(n,k) + 2*A277080(n,k) + 2*A277081(n,k) + 2*A277085(n,k) + A277083(n,k)).


EXAMPLE

Triangle starts:
1, 1;
1, 1;
1, 1, 1;
1, 2, 5, 5, 5, 2, 1;


CROSSREFS

Rows lengths give A038507.
Cf. A277080, A277081, A277083, A277085.
Sequence in context: A197004 A116698 A246900 * A229710 A240947 A023398
Adjacent sequences: A277083 A277084 A277085 * A277087 A277088 A277089


KEYWORD

nonn,tabf


AUTHOR

Christian Bean, Sep 28 2016


STATUS

approved



