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A347847 a(n) is the number of (strict) chains of subspaces with ends 0 and (F_11)^n.

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%I A347847 #9 Sep 18 2021 07:44:36
%S A347847 1,13,1863,2939835,51032042341,9744480919457833,
%T A347847 20467619608367348894343,472899301427912499856338638715,
%U A347847 120188439043897767650882899915804254541,336007833514175643082885509533867247163277824513
%N A347847 a(n) is the number of (strict) chains of subspaces with ends 0 and (F_11)^n.
%H A347847 Álvar Ibeas, <a href="/A347847/b347847.txt">Table of n, a(n) for n = 1..40</a>
%F A347847 a(n) = Sum_{L partition of n} A347492(n, L) * A036038(len(L), sig(L)), where sig(L) is the partition composed by the part multiplicities of L.
%e A347847 a(3) = 1863 = 1 * 1 + 133 * 2 + 1596 * 1, counting:
%e A347847 the unrefined chain 0 < (F_11)^3;
%e A347847 133 chains 0 < V < (F_11)^3, with dim(V) = 1; another
%e A347847 133 chains 0 < V < (F_11)^3, with dim(V) = 2; and
%e A347847 1596 chains 0 < V_1 < V_2 < (F_11)^3.
%Y A347847 Cf. A289545, A347492, A036038.
%K A347847 nonn
%O A347847 1,2
%A A347847 _Álvar Ibeas_, Sep 15 2021