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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. 3
1, 1, 7, 74, 1060, 19013, 408650, 10219360, 291158230, 9302358947, 329192040880, 12775809098058, 539351216354728, 24600280965461923, 1205263251360664310, 63115789721408960624, 3517483455875467926588, 207834769804597591153769, 12976002600530598793672490 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = A138177(2n,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(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-Fran├žois Alcover, Feb 25 2017, translated from Maple *)

CROSSREFS

Cf. A138177, A268309.

Sequence in context: A114472 A000901 A295245 * A098118 A097821 A054745

Adjacent sequences:  A266302 A266303 A266304 * A266306 A266307 A266308

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 31 2016

STATUS

approved

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Last modified August 24 22:41 EDT 2019. Contains 326314 sequences. (Running on oeis4.)