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 A051459 Number of orderings of the subsets of a set with n elements that are compatible with the subsets' sizes; i.e., if A, B are two subsets with A <= B then Card(A) <= Card(B). 6
 1, 1, 2, 36, 414720, 189621927936000000, 2156695499113014719143826715127578624000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(7) has 127 digits and too large to include in sequence. - Ray Chandler, Nov 22 2003 From Valentin Bakoev, Nov 20 2017, May 17 2019: (Start) a(n) is the number of possible orderings of the vectors of the n-dimensional Boolean cube (hypercube) {0,1}^n in accordance with their (Hamming) weights. For arbitrary vectors u, v of {0, 1}^n, if wt(u) mul(binomial(n, i)!, i=0..n): seq(a(n), n=0..6); # Alois P. Heinz, Nov 20 2017 MATHEMATICA Array[Product[Binomial[#, i]!, {i, #}] &, 7, 0] (* Michael De Vlieger, Nov 20 2017 *) PROG (Maxima) a(n):= prod(binomial(n, k)!, k, 0, n); /* Valentin Bakoev, May 17 2019 */ (PARI) a(n) = prod(k=0, n, binomial(n, k)!); \\ Michel Marcus, May 18 2019 CROSSREFS Cf. A000722, A001142, A022914, A294648. Sequence in context: A306644 A283261 A280420 * A358972 A073581 A078081 Adjacent sequences: A051456 A051457 A051458 * A051460 A051461 A051462 KEYWORD nonn AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 15 2003 EXTENSIONS More terms from Ray Chandler, Nov 22 2003 a(0)=1 prepended by Alois P. Heinz, Nov 20 2017 STATUS approved

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Last modified April 19 08:08 EDT 2024. Contains 371782 sequences. (Running on oeis4.)