A266305 Number of n X n symmetric matrices with nonnegative integer entries and without zero rows or columns such that the sum of all entries is equal to 2n.

1, 1, 7, 74, 1060, 19013, 408650, 10219360, 291158230, 9302358947, 329192040880, 12775809098058, 539351216354728, 24600280965461923, 1205263251360664310, 63115789721408960624, 3517483455875467926588, 207834769804597591153769, 12976002600530598793672490

Offset: 0

Author

Alois P. Heinz, Jan 31 2016

Keywords

• nonn

Examples

			a(2) = 7:
  [1 1]  [2 1]  [0 1]  [2 0]  [0 2]  [3 0]  [1 0]
  [1 1]  [1 0]  [1 2]  [0 2]  [2 0]  [0 1]  [0 3].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A138177, A268309.

Programs

Maple

gf:= k-> 1/((1-x)^k*(1-x^2)^(k*(k-1)/2)):
A:= (n, k)-> coeff(series(gf(k), x, n+1), x, n):
a:= n-> add(A(2*n, n-j)*(-1)^j*binomial(n, j), j=0..n):
seq(a(n), n=0..20);

Mathematica

gf[k_] := 1/((1-x)^k*(1-x^2)^(k*(k-1)/2)); A[n_, k_] := SeriesCoefficient[ gf[k], {x, 0, n}]; a[n_] := Sum[A[2*n, n-j]*(-1)^j*Binomial[n, j], {j, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 25 2017, translated from Maple *)

Formula

a(n) = A138177(2n,n).