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A057003
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Write the natural numbers in groups: 1; 2,3; 4,5,6; 7,8,9,10; ... and multiply the members of each group.
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11
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1, 6, 120, 5040, 360360, 39070080, 5967561600, 1220096908800, 321570878428800, 106137499051584000, 42873948150095462400, 20803502274492921984000, 11938961126118491232768000, 7998487694738166709923840000, 6185983879158893706209144832000
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OFFSET
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1,2
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COMMENTS
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Each group begins with a triangular number + 1 and proceeds until the next triangular number.
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LINKS
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FORMULA
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(n (n + 1)/2)!/((n - 1) n /2)!.
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MAPLE
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a:= n-> binomial(n*(n+1)/2, n) * n!:
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MATHEMATICA
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Table[(n (n + 1)/2)!/((n - 1) n /2)!, {n, 1, 15}]
With[{nn=15}, Times@@@TakeList[Range[(nn(nn+1))/2], Range[nn]]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Sep 21 2017 *)
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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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