A268309 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 n^2.

1, 1, 7, 347, 83785, 85813461, 362302219609, 6227015262941276, 433865390872310453097, 122285854086662347886884837, 139236232279790897112737794283927, 639720298831885406784643598607618757713, 11848024220605180271987429760766015754937928643

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..45

Formula

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

Example

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].

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(n^2, n-j)*(-1)^j*binomial(n, j), j=0..n):
seq(a(n), n=0..15);

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[n^2, n-j]*(-1)^j*Binomial[n, j], {j, 0, n}]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 25 2017, translated from Maple *)

Crossrefs

Cf. A138177, A266305.

Sequence in context: A194504 A347505 A015479 * A234622 A142669 A239717

Adjacent sequences: A268306 A268307 A268308 * A268310 A268311 A268312

Keyword

nonn

Author

Alois P. Heinz, Jan 31 2016

Status

approved