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A087047 a(n) = n*(n+1)*(n+2)*a(n-1)/6 for n >= 2; a(1) = 1. 3
1, 4, 40, 800, 28000, 1568000, 131712000, 15805440000, 2607897600000, 573737472000000, 164088916992000000, 59728365785088000000, 27176406432215040000000, 15218787602040422400000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Product of the first n tetrahedral (or pyramidal) numbers. See 2nd formula. - Alexander Adamchuk, May 19 2006

LINKS

Table of n, a(n) for n=1..14.

Karl Dienger, Beiträge zur Lehre von den arithmetischen und geometrischen Reihen höherer Ordnung, Jahres-Bericht Ludwig-Wilhelm-Gymnasium Rastatt, Rastatt, 1910. [Annotated scanned copy]

Eric Weisstein's World of Mathematics, Tetrahedral Number.

FORMULA

a(n) = 2^(-n-1)*3^(-n)*n!*(n+1)!*(n+2)!.

a(n) = Product_{k=1..n} k*(k+1)*(k+2)/6. a(n) = Product_{k=1..n} A000292(k). - Alexander Adamchuk, May 19 2006

EXAMPLE

a(4) = (1/32)*(1/81)*24*120*720 = 800.

MAPLE

a[1]:=1: for n from 2 to 20 do a[n]:=n*(n+1)*(n+2)*a[n-1]/6 od: seq(a[n], n=1..17); # Emeric Deutsch, Mar 06 2005

seq(mul(binomial(k, 3), k=3..n), n=3..16); # Zerinvary Lajos, Aug 07 2007

MATHEMATICA

Table[Product[k*(k+1)*(k+2)/6, {k, 1, n}], {n, 1, 16}] (* Alexander Adamchuk, May 19 2006 *)

PROG

(Sage)

q=50 # change q for more terms

[2^(-n-1)*3^(-n)*factorial(n)*factorial(n+1)*factorial(n+2) for n in [1..q]] # Tom Edgar, Mar 15 2014

CROSSREFS

Cf. A000292, A006472.

Sequence in context: A140701 A277748 A278590 * A211035 A053514 A325293

Adjacent sequences:  A087044 A087045 A087046 * A087048 A087049 A087050

KEYWORD

nonn,easy

AUTHOR

Enrico T. Federighi (rico125162(AT)aol.com), Aug 08 2003

EXTENSIONS

More terms from Emeric Deutsch, Mar 06 2005

Example and formula corrected by Tom Edgar, Mar 15 2014

STATUS

approved

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Last modified June 16 03:44 EDT 2019. Contains 324145 sequences. (Running on oeis4.)