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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-Fran├žois 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.)