

A277080


Irregular triangle read by rows: T(n,k) = number of size k subsets of S_n that remain unchanged by reverse.


1



1, 1, 1, 1, 1, 0, 1, 1, 0, 3, 0, 3, 0, 1, 1, 0, 12, 0, 66, 0, 220, 0, 495, 0, 792, 0, 924, 0, 792, 0, 495, 0, 220, 0, 66, 0, 12, 0, 1, 1, 0, 60, 0, 1770, 0, 34220, 0, 487635, 0, 5461512, 0, 50063860, 0, 386206920, 0, 2558620845, 0, 14783142660, 0, 75394027566
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OFFSET

0,10


COMMENTS

The reverse of a permutation is the reverse in one line notation. For example the reverse of 43521 is 12534.
T(n,k) is the number of size k bases of S_n which remain unchanged by reverse.


LINKS

Table of n, a(n) for n=0..59.


FORMULA

T(n,k) = C(n!/2, k/2) if k is even and T(n,k) = 0 if k is odd.


EXAMPLE

For n = 4 and k = 2 the subsets that remain unchanged by reverse are {4321, 1234}, {1243, 3421}, {4231, 1324}, {1342, 2431}, {1423, 3241}, {1432, 2341}, {2134, 4312}, {3412, 2143}, {2314, 4132}, {3142, 2413}, {4213, 3124} and {4123, 3214} so T(4,2) = 12.
For n = 3 and k = 4 the subsets that remain unchanged by reverse are {231, 321, 132, 123}, {321, 213, 312, 123} and {231, 132, 312, 213} so T(3,4) = 3.
The triangle starts:
1, 1;
1, 1;
1, 0, 1;
1, 0, 3, 0, 3, 0, 1;


PROG

(Sage) def T(n, k):
if k % 2 == 1:
return 0
return binomial( factorial(n)/2, k/2 )


CROSSREFS

Row lengths give A038507.
Sequence in context: A094901 A030220 A219240 * A055240 A174559 A273128
Adjacent sequences: A277077 A277078 A277079 * A277081 A277082 A277083


KEYWORD

nonn,tabf


AUTHOR

Christian Bean, Sep 28 2016


STATUS

approved



