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A362824 Array read by antidiagonals: T(n,k) is the number of k-tuples of involutions on [n] that pairwise commute. 7
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 4, 1, 1, 1, 8, 10, 10, 1, 1, 1, 16, 22, 52, 26, 1, 1, 1, 32, 46, 232, 196, 76, 1, 1, 1, 64, 94, 976, 1016, 1216, 232, 1, 1, 1, 128, 190, 4000, 4576, 12496, 5944, 764, 1, 1, 1, 256, 382, 16192, 19376, 111376, 73648, 42400, 2620, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,9
COMMENTS
Two involutions x,y on [n] commute if x*y = y*x.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals).
FORMULA
T(0,k) = T(1,k) = 1.
EXAMPLE
Array begins:
===========================================================
n/k| 0 1 2 3 4 5 6 7 ...
---+-------------------------------------------------------
0 | 1 1 1 1 1 1 1 1 ...
1 | 1 1 1 1 1 1 1 1 ...
2 | 1 2 4 8 16 32 64 128 ...
3 | 1 4 10 22 46 94 190 382 ...
4 | 1 10 52 232 976 4000 16192 65152 ...
5 | 1 26 196 1016 4576 19376 79696 323216 ...
6 | 1 76 1216 12496 111376 936976 7680016 62177296 ...
7 | 1 232 5944 73648 716416 6289312 52647904 430723168 ...
...
PROG
(PARI) \\ B(n, k) is A022166.
B(n, k)={polcoef(x^k/prod(j=0, k, 1-2^j*x + O(x*x^n)), n)}
T(n, k)={if(n==0, 1, n!*polcoef(exp(sum(j=0, min(k, logint(n, 2)), B(k, j)*x^(2^j)/2^j, O(x*x^n))), n))}
CROSSREFS
Columns k=0..3 are A000012, A000085, A362819, A362825.
Rows n=2..3 are A000079, A033484.
Main diagonal is A362823.
Sequence in context: A290529 A266349 A219094 * A213268 A291118 A245184
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, May 06 2023
STATUS
approved

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Last modified July 12 08:52 EDT 2024. Contains 374239 sequences. (Running on oeis4.)