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%I #9 Sep 18 2021 07:44:22
%S 1,10,804,518376,2674194448,110368339035808,36440751353074277952,
%T 96254339565438079064819328,2033964285682509941820879401890048,
%U 343839935881726495233403720783311789640192
%N a(n) is the number of (strict) chains of subspaces with ends 0 and (F_8)^n.
%H Álvar Ibeas, <a href="/A347845/b347845.txt">Table of n, a(n) for n = 1..40</a>
%F a(n) = Sum_{L partition of n} A347490(n, L) * A036038(len(L), sig(L)), where sig(L) is the partition composed by the part multiplicities of L.
%e a(3) = 804 = 1 * 1 + 73 * 2 + 657 * 1, counting:
%e the unrefined chain 0 < (F_8)^3;
%e 73 chains 0 < V < (F_8)^3, with dim(V) = 1; another
%e 73 chains 0 < V < (F_8)^3, with dim(V) = 2; and
%e 657 chains 0 < V_1 < V_2 < (F_8)^3.
%Y Cf. A289545, A347490, A036038.
%K nonn
%O 1,2
%A _Álvar Ibeas_, Sep 15 2021