# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a321880 Showing 1-1 of 1 %I A321880 #39 Dec 08 2020 08:37:29 %S A321880 1,1,4,15,44,135,456,1239,3424,8694,27240,65846,171864,406133,960848, %T A321880 2615460,5998416,14304089,32273100,72271516,153768520,385905072, %U A321880 817485768,1841794483,3915726528,8388036950,17125197336,35051814558,78986793592,160176485813 %N A321880 Number of partitions of n into colored blocks of equal parts with colors from a set of size n. %H A321880 Alois P. Heinz, Table of n, a(n) for n = 0..1650 %F A321880 a(n) = [x^n] Product_{j=1..n} (1+(n-1)*x^j)/(1-x^j). %F A321880 a(n) = A321884(n,n). %F A321880 a(n) = Sum_{i=0..floor((sqrt(1+8*n)-1)/2)} n!/(n-i)! * A321878(n,i). %F A321880 a(n) = n * A325916(n) for n > 0, a(n) = 1. %e A321880 a(3) = 15: 3a, 3b, 3c, 2a1a, 2a1b, 2a1c, 2b1a, 2b1b, 2b1c, 2c1a, 2c1b, 2c1c, 111a, 111b, 111c. %p A321880 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, k*add( %p A321880 (t-> b(t, min(t, i-1), k))(n-i*j), j=1..n/i) +b(n, i-1, k))) %p A321880 end: %p A321880 a:= n-> b(n$3): %p A321880 seq(a(n), n=0..31); %t A321880 b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[Function[t, b[t, Min[t, i - 1], k]][n - i j], {j, 1, n/i}] k + b[n, i - 1, k]]]; %t A321880 a[n_] := b[n, n, n]; %t A321880 a /@ Range[0, 31] (* _Jean-François Alcover_, Dec 08 2020, after _Alois P. Heinz_ *) %Y A321880 Main diagonal of A321884. %Y A321880 Cf. A000142, A003056, A321878, A325916. %K A321880 nonn %O A321880 0,3 %A A321880 _Alois P. Heinz_, Aug 27 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE