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A140701 Product of first n centered triangular numbers. 2
1, 4, 40, 760, 23560, 1083760, 69360640, 5895654400, 642626329600, 87397180825600, 14507932017049600, 2887078471392870400, 678463440777324544000, 185898982772986925056000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For analog with centered n-gonal numbers, see A140702. For analog with regular (not centered) triangular numbers see polygorial(n,3) = A006472. For the analog with a partial sum instead of a partial product, see A006003.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..244

Eric W. Weisstein, Centered Triangular Number

FORMULA

a(n) = PRODUCT[k=1..n] A005448(k) = PRODUCT[k=1..n] (3*n^2 + 3*n + 2)/2 = PRODUCT[k=1..n] ((3*n*(n-1)/2) + 1).

a(n) ~ cosh(Pi*sqrt(5/3)/2) * 3^n * n^(2*n) / (exp(2*n) * 2^(n-1)). - Vaclav Kotesovec, Jul 11 2015

EXAMPLE

a(10) = 87397180825600 = 1 * 4 * 10 * 19 * 31 * 46 * 64 * 85 * 109 * 136.

MATHEMATICA

Table[Product[(3*k^2-3*k+2)/2, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Jul 11 2015 *)

FoldList[Times, 3*Accumulate[Range[0, 20]]+1] (* Harvey P. Dale, Aug 05 2018 *)

CROSSREFS

Cf. A005448, A006003, A006472, A140702.

Sequence in context: A010792 A064422 A258662 * A277748 A278590 A087047

Adjacent sequences:  A140698 A140699 A140700 * A140702 A140703 A140704

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 24 2008

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)