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A275313 Number of set partitions of [n] where adjacent blocks differ in size. 9
1, 1, 1, 4, 7, 23, 100, 333, 1443, 6910, 36035, 186958, 1095251, 6620976, 42151463, 290483173, 2030271491, 15044953241, 116044969497, 930056879535, 7749440529803, 66931578540965, 597728811956244, 5511695171795434, 52578231393128128, 515775207055816041 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..580

Wikipedia, Partition of a set

EXAMPLE

a(3) = 4: 123, 12|3, 13|2, 1|23.

a(4) = 7: 1234, 123|4, 124|3, 134|2, 1|234, 1|23|4, 1|24|3.

a(5) = 23: 12345, 1234|5, 1235|4, 123|45, 1245|3, 124|35, 125|34, 12|345, 12|3|45, 1345|2, 134|25, 135|24, 13|245, 13|2|45, 145|23, 14|235, 15|234, 1|2345, 1|234|5, 1|235|4, 14|2|35, 1|245|3, 15|2|34.

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, add(`if`(i=j, 0,

      b(n-j, `if`(j>n-j, 0, j))*binomial(n-1, j-1)), j=1..n))

    end:

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

seq(a(n), n=0..35);

MATHEMATICA

b[n_, i_] := b[n, i] = If[n==0, 1, Sum[If[i==j, 0, b[n-j, If[j>n-j, 0, j]]* Binomial[n-1, j-1]], {j, 1, n}]]; a[n_] := b[n, 0]; Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, Dec 18 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A007837, A038041, A275309, A275310, A275311, A275312, A275679, A280275, A286072.

Sequence in context: A270238 A027946 A242315 * A288299 A288763 A203230

Adjacent sequences:  A275310 A275311 A275312 * A275314 A275315 A275316

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 22 2016

STATUS

approved

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Last modified July 29 14:30 EDT 2021. Contains 346346 sequences. (Running on oeis4.)