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A379439 Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).

%I A379439 #13 Jan 20 2025 20:24:15
%S A379439 1,2,4,1,14,6,52,40,4,248,320,76,1416,2946,1395,82,9172,29364,24950,
%T A379439 4348,66366,309558,427336,160050,7258,518868,3365108,6987100,4696504,
%U A379439 688976,4301350,37246245,109761827,118353618,37466297,1491629,37230364,416751008,1668376886,2675297588,1512650776,195728778
%N A379439 Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).
%H A379439 Andrew Howroyd, <a href="/A379439/b379439.txt">Table of n, a(n) for n = 0..120</a> (rows 0..20)
%H A379439 Evgeniy Krasko and Alexander Omelchenko, <a href="https://arxiv.org/abs/1712.10139">Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus</a>, arXiv:1712.10139 [math.CO], 2017, see Appendix Table 4.
%F A379439 T(n,k) = (A379438(n,k) + A380234(n,k))/2.
%e A379439 Triangle begins:
%e A379439   n\k     [0]      [1]      [2]      [3]     [4]
%e A379439   [0]      1;
%e A379439   [1]      2;
%e A379439   [2]      4,       1;
%e A379439   [3]     14,       6;
%e A379439   [4]     52,      40,       4;
%e A379439   [5]    248,     320,      76;
%e A379439   [6]   1416,    2946,    1395,      82;
%e A379439   [7]   9172,   29364,   24950,    4348;
%e A379439   [8]  66366,  309558,  427336,  160050,   7258;
%e A379439   [9] 518868, 3365108, 6987100, 4696504, 688976;
%Y A379439 Row sums are A214816.
%Y A379439 Columns 0..8 are A006385, A006387, A214814, A214815, A297880, A297881, A348798, A348800, A348801.
%Y A379439 Cf. A269919 (rooted), A379438 (sensed), A380234 (achiral), A380235.
%K A379439 nonn,tabf
%O A379439 0,2
%A A379439 _Andrew Howroyd_, Jan 16 2025