# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a328155 Showing 1-1 of 1 %I A328155 #10 May 04 2020 07:04:44 %S A328155 0,0,0,1,4,10,60,35,336,1848,16080,33825,93280,539396,3856216, %T A328155 49390250,147478800,708041160,2354289744,18196716309,150847235040, %U A328155 2615953578700,9488756856040,57565330671310,296745669669768,1435526275752900,12231628020365000 %N A328155 Number of set partitions of [n] with distinct block sizes and one of the block sizes is 3. %H A328155 Alois P. Heinz, Table of n, a(n) for n = 0..697 %H A328155 Wikipedia, Multinomial coefficients %H A328155 Wikipedia, Partition (number theory) %H A328155 Wikipedia, Partition of a set %p A328155 b:= proc(n, i, k) option remember; `if`(i*(i+1)/2 b(n$2, 0)-b(n$2, 3): %p A328155 seq(a(n), n=0..29); %t A328155 b[n_, i_, k_] := b[n, i, k] = If[i(i+1)/2 < n, 0, If[n == 0, 1, If[i < 2, 0, b[n, i - 1, If[i == k, 0, k]]] + If[i == k, 0, b[n - i, Min[n - i, i - 1], k]*Binomial[n, i]]]]; %t A328155 a[n_] := b[n, n, 0] - b[n, n, 3]; %t A328155 a /@ Range[0, 29] (* _Jean-François Alcover_, May 04 2020, after Maple *) %Y A328155 Column k=3 of A327869. %Y A328155 Cf. A328153. %K A328155 nonn %O A328155 0,5 %A A328155 _Alois P. Heinz_, Oct 05 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE