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A177784 a(n) = binomial(n^2, n) / ( n*(n+1) ). 3
1, 7, 91, 1771, 46376, 1533939, 61474519, 2898753715, 157366449604, 9672348219898, 664226242466073, 50419551102990876, 4193002458968329488, 379189865879906158731, 37054233830964389244975 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

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

LINKS

Table of n, a(n) for n=2..16.

EXAMPLE

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

MAPLE

A177784 := proc(n)

        binomial(n^2, n)/(n^2+n) ;

end proc:

seq(A177784(n), n=2..20) ; # R. J. Mathar, Nov 07 2011

CROSSREFS

Sequence in context: A131940 A008542 A121940 * A326266 A124557 A195213

Adjacent sequences:  A177781 A177782 A177783 * A177785 A177786 A177787

KEYWORD

nonn

AUTHOR

Michel Lagneau, May 13 2010

STATUS

approved

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Last modified May 28 11:40 EDT 2020. Contains 334681 sequences. (Running on oeis4.)