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A380616 Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.

%I A380616 #6 Jan 28 2025 20:51:24
%S A380616 1,1,1,2,2,1,5,8,5,2,17,33,30,13,3,79,198,208,118,35,6,554,1571,1894,
%T A380616 1232,472,104,12,5283,16431,21440,15545,6879,1914,315,27,65346,213831,
%U A380616 296952,233027,115134,37311,7881,1021,65,966156,3288821,4799336,4019360,2163112,787065,196267,32857,3407,175
%N A380616 Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.
%C A380616 By duality, also the number of unsensed combinatorial maps with n edges and k faces.
%F A380616 T(n,k) = (A380615(n,k) + A380617(n,k))/2.
%e A380616 Triangle begins:
%e A380616 n\k |     1       2       3       4       5      6     7     8   9
%e A380616 ----+--------------------------------------------------------------
%e A380616   0 |     1;
%e A380616   1 |     1,      1;
%e A380616   2 |     2,      2,      1;
%e A380616   3 |     5,      8,      5,      2;
%e A380616   4 |    17,     33,     30,     13,      3;
%e A380616   5 |    79,    198,    208,    118,     35,     6;
%e A380616   6 |   554,   1571,   1894,   1232,    472,   104,   12;
%e A380616   7 |  5283,  16431,  21440,  15545,   6879,  1914,  315,   27;
%e A380616   8 | 65346, 213831, 296952, 233027, 115134, 37311, 7881, 1021, 65;
%e A380616   ...
%Y A380616 Row sums are A214816.
%Y A380616 Main diagonal is A006082(n+1).
%Y A380616 Columns 1..3 are A054499, A380620, A380621.
%Y A380616 Cf. A053979 (rooted), A277741 (planar), A380615 (sensed), A380617 (achiral).
%K A380616 nonn,tabl
%O A380616 0,4
%A A380616 _Andrew Howroyd_, Jan 28 2025