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A290384 Number of ordered set partitions of [n] such that the smallest element of each block is odd. 2
1, 1, 1, 3, 5, 23, 57, 355, 1165, 9135, 37313, 352667, 1723605, 19063207, 108468169, 1374019539, 8920711325, 127336119839, 928899673425, 14751357906571, 119445766884325, 2088674728868631, 18588486479073881, 354892573941671363, 3443175067395538605 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

All terms are odd.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..494

Wikipedia, Partition of a set

EXAMPLE

a(3) = 3: 123, 12|3, 3|12.

a(4) = 5: 1234, 124|3, 3|124, 12|34, 34|12.

MAPLE

b:= proc(n, m, t) option remember; `if`(n=0, m!,

      add(b(n-1, max(m, j), 1-t), j=1..m+1-t))

    end:

a:= n-> b(n, 0$2):

seq(a(n), n=0..30);

MATHEMATICA

b[n_, m_, t_]:=b[n, m, t]=If[n==0, m!, Sum[b[n - 1, Max[m, j], 1 - t], {j, m + 1 - t}]]; Table[b[n, 0, 0], {n, 0, 50}] (* Indranil Ghosh, Jul 30 2017 *)

CROSSREFS

Cf. A000246, A000670, A290383.

Sequence in context: A120937 A075307 A100302 * A023247 A027753 A066411

Adjacent sequences:  A290381 A290382 A290383 * A290385 A290386 A290387

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 28 2017

STATUS

approved

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Last modified August 19 08:57 EDT 2017. Contains 290794 sequences.