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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 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 September 20 09:38 EDT 2021. Contains 347579 sequences. (Running on oeis4.)