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A322877 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals four. 2
0, 1, 11, 77, 493, 3124, 20019, 130916, 878249, 6063134, 43144661, 316670184, 2397764986, 18726889938, 150814853887, 1251834352246, 10703915163764, 94227518620167, 853463133257984, 7948557602950239, 76069254546156710, 747596311576859585, 7540213445348427312 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..584

Wikipedia, Partition of a set

FORMULA

a(n) = A287254(n) - A287253(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))(4):

seq(a(n), n=4..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 = 4}, A[n, k] - A[n, k - 1]];

a /@ Range[4, 30] (* Jean-François Alcover, May 05 2020, after Maple *)

CROSSREFS

Column k=4 of A287215.

Cf. A287253, A287254.

Sequence in context: A022639 A000589 A211830 * A226708 A206529 A118936

Adjacent sequences:  A322874 A322875 A322876 * A322878 A322879 A322880

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 29 2018

STATUS

approved

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Last modified August 3 17:26 EDT 2020. Contains 336200 sequences. (Running on oeis4.)