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%I #11 Oct 16 2018 23:12:03
%S 1,5,55,430,3605,25980,203280,1417530,10373080,71595830,501688880,
%T 3376856755,23181027055,153326091805,1024829902855,6713038952355,
%U 44092634675905,284723995000530,1845944380173205,11791816763005330,75485171060740630,478105767714603130
%N Number of plane partitions of n where parts are colored in (at most) 5 colors.
%C a(0) = 1 corresponds to the empty sum, in which all terms are colored in one among five given colors, since there is no term at all.
%H M. F. Hasler, <a href="/A306095/b306095.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = Sum_{k=1..n} A091298(n,k)*5^k.
%e For n = 1, there is only the partition [1], which can be colored in any of the five colors, whence a(1) = 5.
%e For n = 2, there are the partitions [2], [1,1] and [1;1]. Adding colors, this yields a(2) = 5 + 25 + 25 = 55 distinct possibilities.
%o (PARI) a(n)=!n+sum(k=1,n,A091298(n,k)*5^k)
%Y Cf. A091298, A208447.
%Y Column 5 of A306100 and A306101. See A306099, A306093, A306094, A306096 for columns 2, 3, 4 and 6.
%K nonn
%O 0,2
%A _M. F. Hasler_, Sep 22 2018
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