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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. Cf. A022166, A362648. Sequence in context: A290529 A266349 A219094 * A213268 A291118 A245184 Adjacent sequences: A362821 A362822 A362823 * A362825 A362826 A362827 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.)