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A272495 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to five.

%I A272495 #7 Dec 11 2020 08:01:24
%S A272495 1,6,63,560,5922,61992,739662,9086616,122792670,1741884144,
%T A272495 26631631026,428931318816,7362963616008,132977285400960,
%U A272495 2538822785931432,50863863365419104,1070731366348427784,23576426902769412672,542918591829347774040,13035693339696004705728
%N A272495 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to five.
%H A272495 Alois P. Heinz, <a href="/A272495/b272495.txt">Table of n, a(n) for n = 5..450</a>
%F A272495 E.g.f.: x^5 * Product_{i=1..5} (i-1)!/(i!-x^i).
%p A272495 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A272495        b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
%p A272495     end:
%p A272495 a:= n-> (k-> b(n, k) -b(n, k-1))(5):
%p A272495 seq(a(n), n=5..30);
%t A272495 b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + If[i > n, 0, Binomial[n, i]*b[n - i, i]]]];
%t A272495 a[n_] := b[n, 5] - b[n, 4];
%t A272495 a /@ Range[5, 30] (* _Jean-François Alcover_, Dec 11 2020, after _Alois P. Heinz_ *)
%Y A272495 Column k=5 of A262071.
%K A272495 nonn
%O A272495 5,2
%A A272495 _Alois P. Heinz_, May 01 2016