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A370059 Number of traceless symmetric binary matrices with 2n 1's and all row sums >= 2.

%I A370059 #13 Feb 09 2024 12:48:57
%S A370059 1,0,0,1,3,18,156,1555,17907,234031,3414375,54984258,968680368,
%T A370059 18532158756,382616109012,8479409847277,200776196593073,
%U A370059 5058600736907013,135130222251100358,3814891312969572209,113492694557655580989,3548800852807887882157,116359373033373284971070
%N A370059 Number of traceless symmetric binary matrices with 2n 1's and all row sums >= 2.
%H A370059 Andrew Howroyd, <a href="/A370059/b370059.txt">Table of n, a(n) for n = 0..200</a>
%e A370059 The a(3) = 1 matrix is:
%e A370059   [0 1 1]
%e A370059   [1 0 1]
%e A370059   [1 1 0]
%e A370059 The a(4) = 3 matrices are:
%e A370059   [0 0 1 1]  [0 1 0 1]  [0 1 1 0]
%e A370059   [0 0 1 1]  [1 0 1 0]  [1 0 0 1]
%e A370059   [1 1 0 0]  [0 1 0 1]  [1 0 0 1]
%e A370059   [1 1 0 0]  [1 0 1 0]  [0 1 1 0]
%o A370059 (PARI) G(n)={my(A=x/exp(x*y + O(x*x^n))); exp(y*x^2/2 - x + O(x*x^n)) * sum(k=0, n, (1 + y + O(y*y^n))^binomial(k, 2)*A^k/k!)}
%o A370059 seq(n)={Vec(subst(Pol(serlaplace(G(n))), x, 1))}
%Y A370059 Row sums of A369931.
%Y A370059 Cf. A001205 (row sums of matrices exactly 2).
%K A370059 nonn
%O A370059 0,5
%A A370059 _Andrew Howroyd_, Feb 08 2024