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A203428
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Reciprocal of Vandermonde determinant of (1/3,1/6,...,1/(3n)).
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3
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1, -6, -486, 839808, 42515280000, -80335512599040000, -6890065294166289123840000, 31601087581187838970614157148160000, 8925080517850366815864624583251321642024960000
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OFFSET
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1,2
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COMMENTS
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Each term divides its successor, as in A203429.
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LINKS
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FORMULA
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a(n) = (-3)^binomial(n,2) * (Gamma(n+1))^(n-1) / BarnesG(n+1). - G. C. Greubel, Sep 28 2023
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MATHEMATICA
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(* First program *)
f[j_]:= 1/(3*j); z = 16;
v[n_]:= Product[Product[f[k] - f[j], {j, k-1}], {k, 2, n}]
1/Table[v[n], {n, z}] (* A203428 *)
Table[v[n]/(3*v[n+1]), {n, z}] (* A203429 *)
(* Second program *)
Table[(-3)^Binomial[n, 2]*(Gamma[n+1])^(n-1)/BarnesG[n+1], {n, 20}] (* G. C. Greubel, Sep 28 2023 *)
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PROG
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(Magma)
Barnes:= func< n | (&*[Factorial(j): j in [1..n-1]]) >;
A203428:= func< n | (-3)^Binomial(n, 2)*(Factorial(n))^n/Barnes(n+1) >;
(SageMath)
def barnes(n): return product(factorial(j) for j in range(n))
def A203428(n): return (-3)^binomial(n, 2)*(factorial(n))^n/barnes(n+1)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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