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A290383 Number of set partitions of [n] such that the smallest element of each block is odd. 2
1, 1, 1, 2, 3, 8, 17, 56, 151, 584, 1893, 8360, 31499, 155720, 666169, 3633704, 17351967, 103284296, 543441005, 3499082408, 20079329875, 138860069192, 861908850561, 6364334129192, 42439075349543, 332934707138888, 2371469004695797, 19681714722718376 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) + n is odd for all n > 1.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..607

Wikipedia, Partition of a set

EXAMPLE

a(3) = 2: 123, 12|3.

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

a(5) = 8: 12345, 1234|5, 1245|3, 124|35, 124|3|5, 125|34, 12|345, 12|34|5.

a(6) = 17: 123456, 12346|5, 1234|56, 12456|3, 1245|36, 1246|35, 124|356, 1246|3|5, 124|36|5, 124|3|56, 1256|34, 125|346, 126|345, 12|3456, 126|34|5, 12|346|5, 12|34|56.

MAPLE

b:= proc(n, m, t) option remember; `if`(n=0, 1,

      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, 1, Sum[b[n - 1, Max[m, j], 1 - t], {j, m + 1 - t}]]; Table[b[n, 0, 0], {n, 0, 50}] (* Indranil Ghosh, Jul 29 2017, after Maple code *)

CROSSREFS

Cf. A000110, A000246, A290384.

Sequence in context: A148035 A148036 A148037 * A099960 A218090 A101182

Adjacent sequences:  A290380 A290381 A290382 * A290384 A290385 A290386

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.