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 A176037 a(n) = n!*(n+1)!*(n+2)!. 2
 2, 12, 288, 17280, 2073600, 435456000, 146313216000, 73741860864000, 53094139822080000, 52563198423859200000, 69383421919494144000000, 119061952013851951104000000, 260031303198252661211136000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is the 3rd sequence in the supersequence whose first member is A000142(n) = n! and whose 2nd member is A010790(n) = n!*(n+1)!. Stirling's approximation is n! ~ ((2*pi*n)^(1/2))*(n^n)*(e^(-n)). Hence n!*(n+1)!*(n+2)! ~ (((2*pi*n)^(1/2))*(n^n)*(e^(-n)))*(((2*pi*(n+1))^(1/2))*((n+1)^(n+1))*(e^(-(n+1))))*(((2*pi*(n+2))^(1/2))*((n+2)^(n+2))*(e^(-(n+2)))) which may be further simplified. Note that n^n = A000312(n). LINKS FORMULA a(n) = n!*(n+1)!*(n+2)! = A000142(n)*A000142(n+1)*A000142(n+2) = A010790(n)*A000142(n+2) = (PRODUCT[i=0..n] i) * (PRODUCT[i=0..n+1] i) * (PRODUCT[i=0..n+2] i). EXAMPLE a(2) = (2)!*(2+1)!*(2+2)! = (2)!*(3)!*(4)! = 2*6*24 = 288. MATHEMATICA Times@@@Partition[Range[0, 15]!, 3, 1] (* Harvey P. Dale, Aug 29 2012 *) CROSSREFS Cf. A000142, A000312, A010790. Sequence in context: A083568 A003121 A211937 * A057170 A200564 A008338 Adjacent sequences:  A176034 A176035 A176036 * A176038 A176039 A176040 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Apr 07 2010 STATUS approved

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Last modified August 5 20:11 EDT 2021. Contains 346488 sequences. (Running on oeis4.)