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A177784
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a(n) = binomial(n^2, n) / ( n*(n+1) ).
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4
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1, 7, 91, 1771, 46376, 1533939, 61474519, 2898753715, 157366449604, 9672348219898, 664226242466073, 50419551102990876, 4193002458968329488, 379189865879906158731, 37054233830964389244975
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OFFSET
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2,2
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COMMENTS
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All terms are integer because n and n+1 divide the binomial (cf. A060545, A177234).
Empirical: In the ring of symmetric functions over the fraction field Q(q, t), letting s(n) denote the Schur function indexed by n, a(n)*(-1)^(n+1) is equal to the coefficient of s(n) in nabla^(n)s(n) with q=t=1, where nabla denotes the "nabla operator" on symmetric functions. - John M. Campbell, Nov 18 2017
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LINKS
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EXAMPLE
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For n = 3, binomial(9,3)/(3*4) =84/12 = 7.
For example, the coefficient of s(3) in nabla(nabla(nabla(s(3)))) is equal to q^6*t^2+q^5*t^3+q^4*t^4+q^3*t^5+q^2*t^6+q^4*t^3+q^3*t^4, and if we let q and t be equal to 1, this coefficient reduces to 7 = a(3). - John M. Campbell, Nov 18 2017
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MAPLE
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binomial(n^2, n)/(n^2+n) ;
end proc:
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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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