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A275423 Number of set partitions of [n] such that five is a multiple of each block size. 2

%I

%S 1,1,1,1,1,2,7,22,57,127,379,1849,9109,37324,128129,507508,3031393,

%T 19609773,108440893,500515633,2467616641,17154715726,134519207131,

%U 927764339426,5359830269641,31580724696907,248587878630807,2259650025239257,18541914182165557

%N Number of set partitions of [n] such that five is a multiple of each block size.

%H Alois P. Heinz, <a href="/A275423/b275423.txt">Table of n, a(n) for n = 0..619</a>

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

%F E.g.f.: exp(x+x^5/5!).

%e a(6) = 7: 12345|6, 12346|5, 12356|4, 12456|3, 13456|2, 1|23456, 1|2|3|4|5|6.

%p a:= proc(n) option remember; `if`(n=0, 1, add(

%p `if`(j>n, 0, a(n-j)*binomial(n-1, j-1)), j=[1, 5]))

%p end:

%p seq(a(n), n=0..30);

%t a[n_] := a[n] = If[n == 0, 1, Sum[If[j > n, 0, a[n-j]*Binomial[n-1, j-1]], {j, {1, 5}}]];

%t Table[a[n], {n, 0, 30}] (* _Jean-Fran├žois Alcover_, May 17 2018, translated from Maple *)

%Y Column k=5 of A275422.

%K nonn

%O 0,6

%A _Alois P. Heinz_, Jul 27 2016

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Last modified December 13 05:16 EST 2018. Contains 318082 sequences. (Running on oeis4.)