cp's OEIS Frontend

A272494 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to four.

%I A272494 #7 Dec 11 2020 07:59:36
%S A272494 1,5,45,350,3290,30870,334950,3765300,46950750,617867250,8815156350,
%T A272494 133031398500,2149039893000,36645888279000,662781093975000,
%U A272494 12612741639498000,252857867367105000,5314211504296695000,117053051989758885000,2693288170000578150000
%N A272494 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to four.
%H A272494 Alois P. Heinz, <a href="/A272494/b272494.txt">Table of n, a(n) for n = 4..450</a>
%F A272494 E.g.f.: x^4 * Product_{i=1..4} (i-1)!/(i!-x^i).
%p A272494 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A272494        b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
%p A272494     end:
%p A272494 a:= n-> (k-> b(n, k) -b(n, k-1))(4):
%p A272494 seq(a(n), n=4..30);
%t A272494 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 A272494 a[n_] := b[n, 4] - b[n, 3];
%t A272494 a /@ Range[4, 30] (* _Jean-François Alcover_, Dec 11 2020, after _Alois P. Heinz_ *)
%Y A272494 Column k=4 of A262071.
%K A272494 nonn
%O A272494 4,2
%A A272494 _Alois P. Heinz_, May 01 2016