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A069945
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Let M_k be the k X k matrix M_k(i,j)=1/binomial(i+n,j); then a(n)=1/det(M_(n+1)).
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2
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1, -6, -360, 252000, 2222640000, -258768639360000, -410299414270986240000, 9061429740221589431500800000, 2835046804394206618956825845760000000, -12733381268715468286016211650968992153600000000
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OFFSET
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1,2
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COMMENTS
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If k>n+1 det(M_k)=0
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LINKS
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FORMULA
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|a(n)| = det(M^(-1)), where M is an n X n matrix with M[i, j]=i/(i+j-1) (or j/(i+j-1)). |a(n)| = 1/det(HilbertMatrix(n))/n! = A005249(n)/n!. - Vladeta Jovovic, Jul 26 2003
|a(n)| = Product_{i=1..2n-1} binomial(i,floor(i/2)). - Peter Luschny, Sep 18 2012
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MATHEMATICA
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a[n_] := (-1)^Quotient[n, 2]/(Det[HilbertMatrix[n]] n!); Array[a, 10] (* Jean-François Alcover, Jul 06 2019 *)
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PROG
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(PARI) for(n=0, 10, print1(1/matdet(matrix(n+1, n+1, i, j, 1/binomial(i+n, j))), ", "))
(Sage)
def A069945(n): return (-1)^(n//2)*mul(binomial(i, i//2) for i in (1..2*n-1))
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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