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A277081 Irregular triangle read by rows: T(n,k) = number of size k subsets of S_n that remain unchanged under the operation of replacing a permutation with its inverse. 1
1, 1, 1, 1, 1, 2, 1, 1, 4, 7, 8, 7, 4, 1, 1, 10, 52, 190, 546, 1302, 2660, 4754, 7535, 10692, 13672, 15820, 16604, 15820, 13672, 10692, 7535, 4754, 2660, 1302, 546, 190, 52, 10, 1, 1, 26, 372, 3822, 31306, 216086, 1300420, 6981650, 33992275, 151945820 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

T(n,k) is the number of size k subsets of S_n that remain unchanged under the operation of replacing a permutation with its inverse.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

T(n,k) = Sum( C((n! - I(n))/2, i)*C(I(n), k - 2*i) for i in [0..floor(k/2)]) where I(n) = A000085(n).

EXAMPLE

For n = 3 and k = 3 the subsets unchanged by inverse are {213,132,123}, {321,132,123}, {321,213,123}, {231,312,123}, {321,132,213}, {132,312,231},{213,312,231}, {321,231,312} hence T(3,3) = 8. (Here we are using the one-line notation for permutations, not the product of cycles form.)

Triangle starts:

1, 1;

1, 1;

1, 2, 1;

1, 4, 7, 8, 7, 4, 1;

CROSSREFS

Row lengths give A038507.

Cf. A000085.

Sequence in context: A265232 A011016 A096540 * A111569 A213786 A055130

Adjacent sequences:  A277078 A277079 A277080 * A277082 A277083 A277084

KEYWORD

nonn,tabf,more

AUTHOR

Christian Bean, Sep 28 2016

STATUS

approved

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Last modified December 11 18:46 EST 2019. Contains 329925 sequences. (Running on oeis4.)