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A306101 Square array T(n,k) = number of plane partitions of n with parts colored in (at most) k colors; n, k >= 1; read by antidiagonals.

%I A306101 #26 Sep 26 2018 15:27:02
%S A306101 1,2,3,3,10,6,4,21,34,13,5,36,102,122,24,6,55,228,525,378,48,7,78,430,
%T A306101 1540,2334,1242,86,8,105,726,3605,8964,11100,3690,160,9,136,1134,7278,
%U A306101 25980,56292,47496,11266,282,10,171,1672,13237,62574,203280,316388,210756,32666,500,11,210,2358,22280,132258,586878,1417530
%N A306101 Square array T(n,k) = number of plane partitions of n with parts colored in (at most) k colors; n, k >= 1; read by antidiagonals.
%C A306101 One could have included a row 0 with all 1's, since there is exactly one partition of n = 0, the empty sum, for which all terms (since there are none) are colored in one among k colors.
%H A306101 Alois P. Heinz, <a href="/A306101/b306101.txt">Antidiagonals n = 1..50, flattened</a>
%F A306101 T(n,k) = Sum_{j=1..n} A091298(n,j)*k^j.
%e A306101 The array starts:
%e A306101   [      1       2       3       4       5 ...] = A000027
%e A306101   [      3      10      21      36      55 ...] = A014105
%e A306101   [      6      34     102     228     430 ...] = A067389
%e A306101   [     13     122     525    1540    3605 ...]
%e A306101   [     24     378    2334    8964   25980 ...]
%e A306101   [     48    1242   11100   56292  203280 ...]
%e A306101    A000219 A306099 A306093 A306094 A306094
%e A306101 For concrete examples, see A306099 and A306093.
%o A306101 (PARI) A306101(n,k)=sum(j=1,n,A091298(n,j)*k^j)
%Y A306101 Cf. A091298, A208447, A000219, A000027, A014105, A067389.
%Y A306101 See A306100 for a variant.
%Y A306101 Cf. A000219, A306099, A306093, A306094, A306095 for columns 1..5.
%K A306101 nonn,tabl
%O A306101 1,2
%A A306101 _M. F. Hasler_, Sep 22 2018