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 A318618 a(n) is the number of rooted forests on n nodes that avoid the patterns 321, 2143, and 3142. 1
 1, 1, 3, 15, 102, 870, 8910, 106470, 1454040, 22339800, 381364200, 7161323400, 146701724400, 3255661609200, 77808668137200, 1992415575150000, 54420258228336000, 1579320261543024000, 48529229906613456000, 1574046971727454224000, 53741325186841612320000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is the number of rooted labeled forests on n nodes so that along any path from the root to a vertex, there is at most one descent. LINKS FORMULA a(n) = n! + Sum_{k=1..n} Sum_{j=1..min(k, n-k)} (n!/2^j)*binomial(n-k-1, j-1)*binomial(k, j). MATHEMATICA a[n_] := n! + Sum[n! 2^-j Binomial[n-k-1, j-1] Binomial[k, j], {k, 1, n}, {j, 1, Min[k, n-k]}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Sep 13 2018 *) PROG (PARI) a(n) = {n! + sum(k=1, n, sum(j=1, min(k, n-k), n!/(2^j)*binomial(n-k-1, j-1)*binomial(k, j)))} \\ Andrew Howroyd, Aug 31 2018 CROSSREFS Cf. A000272, A318617, A007840, A000671, A000262. Sequence in context: A135903 A185753 A174493 * A123184 A079486 A245118 Adjacent sequences:  A318615 A318616 A318617 * A318619 A318620 A318621 KEYWORD nonn AUTHOR Kassie Archer, Aug 30 2018 STATUS approved

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Last modified November 30 10:56 EST 2021. Contains 349419 sequences. (Running on oeis4.)