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A369336
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Number of n X n Fishburn matrices with entries in the set {0,1,...,n}.
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2
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1, 1, 12, 2052, 5684480, 305416893750, 391129148721673152, 14286237711414132094989064, 17309880507327972883933887341789184, 792117985317303404452447777723478865406570410, 1534214120588806182890487155420702132205591283310000000000
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OFFSET
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0,3
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COMMENTS
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Number of upper triangular n X n {0,1,...,n}-matrices with no zero rows or columns.
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LINKS
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FORMULA
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a(n) = [x^n] Sum_{j=0..n} x^j * Product_{i=1..j} ((n+1)^i-1)/(1+x*((n+1)^i-1)).
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EXAMPLE
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a(0) = 1: [].
a(1) = 1: [1].
a(2) = 12:
[10] [10] [20] [20] [11] [11] [21] [21] [12] [12] [22] [22]
[ 1] [ 2] [ 1] [ 2] [ 1] [ 2] [ 1] [ 2] [ 1] [ 2] [ 1] [ 2].
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MAPLE
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a:= n-> coeff(series(add(x^j*mul(((n+1)^i-1)/(1+x*
((n+1)^i-1)), i=1..j), j=0..n), x, n+1), x, n):
seq(a(n), n=0..10);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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