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 A285917 Number of ordered set partitions of [n] into two blocks such that equal-sized blocks are ordered with increasing least elements. 4
 1, 6, 11, 30, 52, 126, 219, 510, 896, 2046, 3632, 8190, 14666, 32766, 59099, 131070, 237832, 524286, 956196, 2097150, 3841586, 8388606, 15425136, 33554430, 61908562, 134217726, 248377154, 536870910, 996183062, 2147483646, 3994427099, 8589934590, 16013066072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS a(n) is odd if and only if n = 2^k with k>0. LINKS Alois P. Heinz, Table of n, a(n) for n = 2..1000 Wikipedia, Partition of a set MAPLE a:= n-> 2*add(binomial(n, k), k=1..n/2)-         `if`(n::even, 3/2*binomial(n, n/2), 0): seq(a(n), n=2..40); # second Maple program: a:= proc(n) option remember; `if`(n<5, [0, 1, 6, 11][n],       (9*(n-1)*(n-4)*a(n-1)+2*(3*n^2-16*n+6)*a(n-2)       -36*(n-2)*(n-4)*a(n-3)+8*(n-3)*(3*n-10)*a(n-4))       /((3*n-13)*n))     end: seq(a(n), n=2..40); MATHEMATICA a[n_] := 2*Sum[Binomial[n, k], {k, 1, n/2}] - If[EvenQ[n], 3/2*Binomial[n, n/2], 0]; Table[a[n], {n, 2, 40}] (* Jean-François Alcover, May 26 2018, from Maple *) PROG (PARI) a(n) = 2*sum(k=1, n\2, binomial(n, k)) - if (!(n%2), 3*binomial(n, n/2)/2); \\ Michel Marcus, May 26 2018 CROSSREFS Column k=2 of A285824. Cf. A285853. Sequence in context: A273857 A034489 A231410 * A105508 A114960 A320482 Adjacent sequences:  A285914 A285915 A285916 * A285918 A285919 A285920 KEYWORD nonn AUTHOR Alois P. Heinz, Apr 28 2017 STATUS approved

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Last modified August 5 22:41 EDT 2021. Contains 346488 sequences. (Running on oeis4.)