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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

%I

%S 0,1,19,171,1293,9320,66992,488526,3637440,27735903,216992278,

%T 1743777862,14401360577,122242150172,1066284279026,9554869690126,

%U 87923414758506,830459368379431,8047463255217118,79967170844047637,814439368083686232,8497321384591725159

%N Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals five.

%H Alois P. Heinz, <a href="/A322878/b322878.txt">Table of n, a(n) for n = 5..582</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

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

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

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

%p end:

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

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

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

%t 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]];

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

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

%t a /@ Range[5, 30] (* _Jean-Fran├žois Alcover_, May 05 2020, after Maple *)

%Y Column k=5 of A287215.

%Y Cf. A287254, A287255.

%K nonn

%O 5,3

%A _Alois P. Heinz_, Dec 29 2018

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Last modified September 18 10:31 EDT 2020. Contains 337166 sequences. (Running on oeis4.)