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A014068
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C( n*(n+1)/2, n).
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6
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1, 1, 3, 20, 210, 3003, 54264, 1184040, 30260340, 886163135, 29248649430, 1074082795968, 43430966148115, 1917283000904460, 91748617512913200, 4730523156632595024, 261429178502421685800, 15415916972482007401455
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Product of next n numbers divided by product of first n numbers. E.g. a(4) = (7*8*9*10)/(1*2*3*4)= 210. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 22 2004
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FORMULA
| For n >=1, product k=1, ...n A014068(n) = A022915(n) - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 08 2001
For n > 0, a(n) = A022915(n)/A022915(n-1) - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jul 26 2004
a(n) = binomial(T(n+1), T(n)) where T(n)= the n-th triangular number. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 14 2005
a(n)=(C(C(n+2,n),n+1)) for -1 to infinity. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 30 2009]
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PROG
| (Other) sage: [(binomial(binomial(n+2, n), n+1)) for n in xrange(-1, 17)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 30 2009]
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CROSSREFS
| Cf. A022915.
Sequence in context: A052590 A081209 A196560 * A006963 A113333 A206405
Adjacent sequences: A014065 A014066 A014067 * A014069 A014070 A014071
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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