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 A365638 Triangular array read by rows: T(n, k) is the number of ways that a k-element transitive tournament can occur as a subtournament of a larger tournament on n labeled vertices. 0
 1, 1, 1, 2, 4, 2, 8, 24, 24, 6, 64, 256, 384, 192, 24, 1024, 5120, 10240, 7680, 1920, 120, 32768, 196608, 491520, 491520, 184320, 23040, 720, 2097152, 14680064, 44040192, 55050240, 27525120, 5160960, 322560, 5040, 268435456, 2147483648, 7516192768, 11274289152, 7046430720, 1761607680, 165150720, 5160960, 40320 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A tournament is a directed digraph obtained by assigning a direction for each edge in an undirected complete graph. In a transitive tournament all nodes can be strictly ordered by their reachability. LINKS Table of n, a(n) for n=0..44. Paul Erdős, On a problem in graph theory, The Mathematical Gazette, 47: 220-223 (1963). FORMULA T(n, k) = binomial(n, k)*k!*2^(binomial(n, 2) - binomial(k, 2)). T(n, 0) = A006125(n). T(n, 1) = A095340(n). T(n, 2) = A103904(n). T(n, n) = n!. T(n, n-1) = A002866(n-1). T(n, n-2) = A052670(n). EXAMPLE Triangle begins: 1 1, 1 2, 4, 2 8, 24, 24, 6 64, 256, 384, 192, 24 1024, 5120, 10240, 7680, 1920, 120 MAPLE T := (n, k) -> 2^(((n-1)*n - (k-1)*k)/2) * n! / (n-k)!: seq(seq(T(n, k), k = 0..n), n = 0..8); # Peter Luschny, Nov 02 2023 PROG (PARI) T(n, k) = binomial(n, k)*k!*2^(binomial(n, 2) - binomial(k, 2)) CROSSREFS Cf. A002866, A006125, A052670, A095340, A103904. Cf. A122027, A224886, A259105, A350608, A350609, A350610. Sequence in context: A229296 A232565 A058942 * A196759 A303165 A188813 Adjacent sequences: A365635 A365636 A365637 * A365639 A365640 A365641 KEYWORD nonn,easy,tabl AUTHOR Thomas Scheuerle, Sep 14 2023 STATUS approved

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Last modified September 11 09:20 EDT 2024. Contains 375814 sequences. (Running on oeis4.)