%I #7 Oct 18 2018 08:49:30
%S 1,6,78,726,7278,62574,586878,4889166,42892710,354335982,2976581670,
%T 23990771094,197564663094,1565310230790,12548473437822,98526949264374,
%U 776195574339102,6008457242324814,46729763436714126,357901583160822990,2748384845416097718
%N Number of plane partitions of n where parts are colored in (at most) 6 colors.
%C a(0) = 1 corresponds to the empty sum, in which all terms are colored in one among six given colors, since there is no term at all.
%H M. F. Hasler, <a href="/A306096/b306096.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = Sum_{k=1..n} A091298(n,k)*6^k, for n > 0.
%e For n = 1, there is only the partition [1], which can be colored in any of the six colors, whence a(1) = 6.
%e For n = 2, there are the partitions [2], [1,1] and [1;1]. Adding colors, this yields a(2) = 6 + 36 + 36 = 78 distinct possibilities.
%o (PARI) a(n)=sum(k=1,n,A091298(n,k)*6^k,!n)
%Y Cf. A091298, A208447.
%Y Column 6 of A306100 and A306101. See A306099, A306093, A306094, A306095 for columns 2, 3, 4 and 5.
%K nonn
%O 0,2
%A _M. F. Hasler_, Oct 16 2018