A362824 Array read by antidiagonals: T(n,k) is the number of k-tuples of involutions on [n] that pairwise commute.
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
Offset: 0
Examples
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 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals).
Crossrefs
Programs
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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))}
Formula
T(0,k) = T(1,k) = 1.
Comments