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Search: id:A107252
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| A107252 |
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Product (n+k)!/(k+1)!, k=0..n-1. |
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2
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| 1, 1, 6, 1440, 36288000, 184354652160000, 309071606732292096000000, 254046582743105184577722777600000000, 142518177743863255019484504453155074867200000000000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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SF(2n-1)/(SF(n)*SF(n-1)) where SF is the superfactorial A000178 product of factorials.
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FORMULA
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a(n) = (n+1)!*(n+2)!*...*(2n-1)!/(1!*2!*...*(n-1)!) = A000178(2n-1)/(A000178(n)*A000178(n-1)) = A079478(n)/A001813(n) = A079478(n-1)*A006963(n+1) = A107251(n)/A000108(n) = A107251(n-1)*A009445(n-1) = A107254(n)/A000142(n) = A009963(2n-1, n-1) = A009963(2n-1, n).
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EXAMPLE
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a(3) = 1!*2!*3!*4!*5!/(1!*2!*3!*1!*2!) = 34560/24 = 1440.
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MATHEMATICA
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Table[Product[(n+k)!/(k+1)!, {k, 0, n-1}], {n, 0, 10}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 10 2006
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CROSSREFS
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Cf. A001700.
Cf. A005130, A110131, A112332.
Sequence in context: A076781 A055306 A066037 this_sequence A131453 A160226 A034841
Adjacent sequences: A107249 A107250 A107251 this_sequence A107253 A107254 A107255
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 14 2005
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