A270496 - OEIS

%I #11 May 27 2018 02:00:39

%S 1,12,97,675,4418,28396,183615,1211936,8237223,57944187,422950882,

%T 3206531728,25247250641,206313943476,1747990803645,15336960025775,

%U 139187730958406,1304967471569208,12624893940830455,125892638744630088,1292581981392588771

%N Sum of the sizes of the fourth blocks in all set partitions of {1,2,...,n}.

%H Alois P. Heinz, <a href="/A270496/b270496.txt">Table of n, a(n) for n = 4..575</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%p b:= proc(n, m) option remember; `if`(n=0, [1, 0],

%p       add((p->`if`(j<5, [p[1], p[2]+p[1]*x^j], p))(

%p        b(n-1, max(m, j))), j=1..m+1))

%p     end:

%p a:= n-> coeff(b(n, 0)[2], x, 4):

%p seq(a(n), n=4..30);

%t b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 5, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];

%t a[n_] := Coefficient[b[n, 0][[2]], x, 4];

%t Table[a[n], {n, 4, 30}] (* _Jean-François Alcover_, May 27 2018, translated from Maple *)

%Y Column p=4 of A270236.

%K nonn

%O 4,2

%A _Alois P. Heinz_, Mar 18 2016