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A286951 Irregular triangle read by rows: T(n,k) is the number of simple graphs with n vertices with matching number k (0 <= k <= floor(n/2)).

%I A286951 #25 Feb 16 2025 08:33:45
%S A286951 1,1,1,1,1,3,1,4,6,1,5,28,1,6,48,101,1,7,73,963,1,8,106,1818,10413,1,
%T A286951 9,147,3383,271128,1,10,198,6129,441031,11557799
%N A286951 Irregular triangle read by rows: T(n,k) is the number of simple graphs with n vertices with matching number k (0 <= k <= floor(n/2)).
%H A286951 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MatchingNumber.html">Matching Number</a>
%e A286951 Triangle begins:
%e A286951   1;
%e A286951   1;
%e A286951   1, 1;
%e A286951   1, 3;
%e A286951   1, 4,  6;
%e A286951   1, 5,  28;
%e A286951   1, 6,  48,  101;
%e A286951   1, 7,  73,  963;
%e A286951   1, 8, 106, 1818, 10413;
%e A286951   ...
%Y A286951 Row sums are A000088.
%Y A286951 T(2n,n) gives A218462 (for n>0).
%K A286951 nonn,tabf
%O A286951 0,6
%A A286951 _Eric W. Weisstein_, May 17 2017
%E A286951 Name corrected by _Andrew Howroyd_, Nov 04 2017
%E A286951 T(0,0)=1 added by _Alois P. Heinz_, Nov 04 2017