cp's OEIS Frontend

A325478 Number of colored set partitions of [n] where colors of the elements of subsets are distinct and in increasing order and all colors of an initial interval of the color palette are used.

%I A325478 #20 Dec 14 2020 08:39:58
%S A325478 1,1,4,29,329,5252,110955,2972769,97922354,3872594811,180459028989,
%T A325478 9759149087646,604841170643957,42508077480226893,3357224252026104140,
%U A325478 295651782273190911233,28834727303442640011901,3095877335697619795977036,363977673792652615285223095
%N A325478 Number of colored set partitions of [n] where colors of the elements of subsets are distinct and in increasing order and all colors of an initial interval of the color palette are used.
%H A325478 Alois P. Heinz, <a href="/A325478/b325478.txt">Table of n, a(n) for n = 0..296</a>
%p A325478 b:= proc(n, k) option remember; `if`(n=0, 1, add(b(n-j, k)*
%p A325478       binomial(n-1, j-1)*binomial(k, j), j=1..min(k, n)))
%p A325478     end:
%p A325478 a:= n-> add(add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k), k=0..n):
%p A325478 seq(a(n), n=0..23);
%t A325478 b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - j, k] Binomial[n - 1, j - 1] Binomial[k, j], {j, 1, Min[k, n]}]];
%t A325478 a[n_] := Sum[Sum[b[n, k - i] (-1)^i Binomial[k, i], {i, 0, k}], {k, 0, n}];
%t A325478 a /@ Range[0, 23] (* _Jean-François Alcover_, Dec 14 2020, after _Alois P. Heinz_ *)
%Y A325478 Row sums of A322670.
%K A325478 nonn
%O A325478 0,3
%A A325478 _Alois P. Heinz_, Sep 06 2019