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A322878 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals five. 2
0, 1, 19, 171, 1293, 9320, 66992, 488526, 3637440, 27735903, 216992278, 1743777862, 14401360577, 122242150172, 1066284279026, 9554869690126, 87923414758506, 830459368379431, 8047463255217118, 79967170844047637, 814439368083686232, 8497321384591725159 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..582

Wikipedia, Partition of a set

FORMULA

a(n) = A287255(n) - A287254(n).

MAPLE

b:= proc(n, k, m, l) option remember; `if`(n<1, 1,

     `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))

    end:

A:= (n, k)-> b(n-1, min(k, n-1), 1, n):

a:= n-> (k-> A(n, k)-A(n, k-1))(5):

seq(a(n), n=5..30);

MATHEMATICA

b[n_, k_, m_, l_] := b[n, k, m, l] = If[n < 1, 1, If[l - n > k, 0, b[n - 1, k, m + 1, n]] + m b[n - 1, k, m, l]];

A[n_, k_] := b[n - 1, Min[k, n - 1], 1, n];

a[n_] := With[{k = 5}, A[n, k] - A[n, k - 1]];

a /@ Range[5, 30] (* Jean-Fran├žois Alcover, May 05 2020, after Maple *)

CROSSREFS

Column k=5 of A287215.

Cf. A287254, A287255.

Sequence in context: A010935 A282288 A022614 * A060222 A041690 A217698

Adjacent sequences:  A322875 A322876 A322877 * A322879 A322880 A322881

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 29 2018

STATUS

approved

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Last modified August 3 14:46 EDT 2020. Contains 336198 sequences. (Running on oeis4.)