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A379438 Triangle read by rows: T(n,k) is the number of sensed combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).

%I A379438 #15 Jan 20 2025 19:14:13
%S A379438 1,2,4,1,14,6,57,46,4,312,452,106,2071,4852,2382,131,15030,52972,
%T A379438 46680,8158,117735,587047,830848,313611,14118,967850,6550808,13804864,
%U A379438 9326858,1369446,8268816,73483256,218353000,236095958,74803564,2976853,72833730,827801468,3328822880,5345316004,3023693380,391288854
%N A379438 Triangle read by rows: T(n,k) is the number of sensed combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).
%H A379438 Andrew Howroyd, <a href="/A379438/b379438.txt">Table of n, a(n) for n = 0..120</a> (rows 0..20)
%H A379438 Antonio Breda d'Azevedo, Alexander Mednykh and Roman Nedela, <a href="https://doi.org/10.1016/j.disc.2009.11.017">Enumeration of maps regardless of genus: Geometric approach</a>, Discrete Mathematics, Volume 310, 2010, Pages 1184-1203.
%H A379438 Timothy R. Walsh, Alain Giorgetti, and Alexander Mednykh, <a href="http://dx.doi.org/10.1016/j.disc.2011.11.027">Enumeration of unrooted orientable maps of arbitrary genus by number of edges and vertices</a>, Discrete Math. 312 (2012), no. 17, 2660--2671. MR2935417.
%e A379438 Triangle begins:
%e A379438   n\k     [0]      [1]       [2]      [3]      [4]
%e A379438   [0]      1;
%e A379438   [1]      2;
%e A379438   [2]      4,       1;
%e A379438   [3]     14,       6;
%e A379438   [4]     57,      46,        4;
%e A379438   [5]    312,     452,      106;
%e A379438   [6]   2071,    4852,     2382,     131;
%e A379438   [7]  15030,   52972,    46680,    8158;
%e A379438   [8] 117735,  587047,   830848,  313611,   14118;
%e A379438   [9] 967850, 6550808, 13804864, 9326858, 1369446;
%e A379438   ...
%Y A379438 Row sums are A170946.
%Y A379438 Columns 0..10 are A006384, A006386, A104595, A104596, A215019, A239918, A239919, A239921, A239922, A239923, A239924.
%Y A379438 Cf. A269919 (rooted), A379439 (unsensed), A380234 (achiral), A380235.
%K A379438 nonn,tabf
%O A379438 0,2
%A A379438 _Andrew Howroyd_, Jan 16 2025