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A057003 Write the natural numbers in groups: 1; 2,3; 4,5,6; 7,8,9,10; ... and multiply the members of each group. 8
1, 6, 120, 5040, 360360, 39070080, 5967561600, 1220096908800, 321570878428800, 106137499051584000, 42873948150095462400, 20803502274492921984000, 11938961126118491232768000, 7998487694738166709923840000, 6185983879158893706209144832000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Each group begins with a triangular number + 1 and proceeds until the next triangular number.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..200

FORMULA

(n (n + 1)/2)!/((n - 1) n /2)!.

MAPLE

a:= n-> binomial(n*(n+1)/2, n) * n!:

seq(a(n), n=1..20);  # Alois P. Heinz, Aug 17 2012

MATHEMATICA

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 *)

CROSSREFS

Cf. A006003.

Sequence in context: A196688 A126448 A126446 * A096718 A096720 A009445

Adjacent sequences:  A057000 A057001 A057002 * A057004 A057005 A057006

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Sep 09 2000

STATUS

approved

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Last modified January 27 02:46 EST 2020. Contains 331291 sequences. (Running on oeis4.)