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Search: id:A123680
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| A123680 |
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a(n) = Sum_{k=0..n} C(n+k-1,k)*k!. |
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+0
3
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| 1, 2, 9, 76, 985, 17046, 366289, 9374968, 278095761, 9375293170, 353906211241, 14785127222724, 677150215857193, 33734100501544366, 1816008001717251105, 105048613959883117936, 6497985798745934394529, 427999600108502895779658
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is divisible by (n+1) : a(n)/(n+1) = A123681(n).
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EXAMPLE
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Since a(n) = Sum_{k=0..n} k! * [x^k] 1/(1-x)^n, to get a(4),
list coefficients of x^0 through x^4 in 1/(1-x)^4, [1,4,10,20,35],
then dot product with factorials 0! through 4!, [0!,1!,2!,3!,4! ],
so that a(4) = 1*0! + 4*1! + 10*2! + 20*3! + 35*4! = 985.
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PROGRAM
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(PARI) a(n)=sum(k=0, n, binomial(n+k-1, k)*k!)
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CROSSREFS
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Cf. A123681.
Sequence in context: A029849 A080638 A105785 this_sequence A132621 A108992 A058164
Adjacent sequences: A123677 A123678 A123679 this_sequence A123681 A123682 A123683
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 05 2006
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EXTENSIONS
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Definition corrected Oct 27 2006
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