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A092985
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a(n) = Arithofactorial(n)= AF(n) is the product of first n terms of an arithmetic progression with the first term 1 and common difference n.
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1
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1, 1, 3, 28, 585, 22176, 1339975, 118514880, 14454403425, 2326680294400, 478015854767451, 122087424094272000, 37947924636264267625, 14105590169042424729600, 6178966019176767549393375
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| We have the triangle
1
1 3
1 4 7
1 5 9 13
1 6 11 16 21
1 7 13 19 25 31
...
Sequence contains the product of the terms of the rows.
a(n) = b(n-1) where b(n) = n^n*Gamma(n+1/n)/Gamma(1/n) and b(0) is limit n->0+ of b(n). - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Nov 10 2007
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FORMULA
| a(n) = 1*(1+n)*(1+2n)*...*(n^2-n+1).
a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling1(n, k)*n^(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 28 2005
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EXAMPLE
| a(5) = 1*6*11*16*21 = 22176.
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CROSSREFS
| Cf. A057237, A092987.
Sequence in context: A062497 A056066 A174483 * A181588 A084880 A110259
Adjacent sequences: A092982 A092983 A092984 * A092986 A092987 A092988
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KEYWORD
| easy,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 28 2004
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EXTENSIONS
| More terms from Erich Friedman (efriedma(AT)stetson.edu), Aug 08 2005
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