A370059 - OEIS

%I #13 Feb 09 2024 12:48:57

%S 1,0,0,1,3,18,156,1555,17907,234031,3414375,54984258,968680368,

%T 18532158756,382616109012,8479409847277,200776196593073,

%U 5058600736907013,135130222251100358,3814891312969572209,113492694557655580989,3548800852807887882157,116359373033373284971070

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

%H Andrew Howroyd, <a href="/A370059/b370059.txt">Table of n, a(n) for n = 0..200</a>

%e The a(3) = 1 matrix is:

%e   [0 1 1]

%e   [1 0 1]

%e   [1 1 0]

%e The a(4) = 3 matrices are:

%e   [0 0 1 1]  [0 1 0 1]  [0 1 1 0]

%e   [0 0 1 1]  [1 0 1 0]  [1 0 0 1]

%e   [1 1 0 0]  [0 1 0 1]  [1 0 0 1]

%e   [1 1 0 0]  [1 0 1 0]  [0 1 1 0]

%o (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 seq(n)={Vec(subst(Pol(serlaplace(G(n))), x, 1))}

%Y Row sums of A369931.

%Y Cf. A001205 (row sums of matrices exactly 2).

%K nonn

%O 0,5

%A _Andrew Howroyd_, Feb 08 2024