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%I #9 Sep 18 2021 07:44:33
%S 1,7,249,44643,40065301,179833594207,4036127700341649,
%T 452932494435315724443,254139954749268142006053901,
%U 712988623255130761190069046824407,10001434425838325885839124865408303623049
%N a(n) is the number of (strict) chains of subspaces with ends 0 and (F_5)^n.
%H Álvar Ibeas, <a href="/A347843/b347843.txt">Table of n, a(n) for n = 1..40</a>
%F a(n) = Sum_{L partition of n} A347488(n, L) * A036038(len(L), sig(L)), where sig(L) is the partition composed by the part multiplicities of L.
%e a(3) = 249 = 1 * 1 + 31 * 2 + 186 * 1, counting:
%e the unrefined chain 0 < (F_5)^3;
%e 31 chains 0 < V < (F_5)^3, with dim(V) = 1; another
%e 31 chains 0 < V < (F_5)^3, with dim(V) = 2; and
%e 186 chains 0 < V_1 < V_2 < (F_5)^3.
%Y Cf. A289545, A347488, A036038.
%K nonn
%O 1,2
%A _Álvar Ibeas_, Sep 15 2021
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