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A266305
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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.
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3
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1, 1, 7, 74, 1060, 19013, 408650, 10219360, 291158230, 9302358947, 329192040880, 12775809098058, 539351216354728, 24600280965461923, 1205263251360664310, 63115789721408960624, 3517483455875467926588, 207834769804597591153769, 12976002600530598793672490
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..200
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FORMULA
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a(n) = A138177(2n,n).
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EXAMPLE
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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].
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MAPLE
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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);
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A138177, A268309.
Sequence in context: A000901 A295245 A341330 * A098118 A097821 A337387
Adjacent sequences: A266302 A266303 A266304 * A266306 A266307 A266308
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Jan 31 2016
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STATUS
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approved
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