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Search: id:A001702
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| A001702 |
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Generalized Stirling numbers.
(Formerly M5148 N2234)
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+0
1
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| 1, 24, 154, 580, 1665, 4025, 8624, 16884, 30810, 53130, 87450, 138424, 211939, 315315, 457520, 649400, 903924, 1236444, 1664970, 2210460, 2897125, 3752749
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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(1/48) (n-1)n(n+1)(n+4)(n^2+7n+14), n>1.
If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n-1) = -f(n,n-3,2), for n>=3. [From Milan R. Janjic (agnus(AT)blic.net), Dec 20 2008]
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MAPLE
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A001702:=(-1-17*z-7*z**2+29*z**3-34*z**4+21*z**5-7*z**6+z**7)/(z-1)**7; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A039494 A159650 A092181 this_sequence A004308 A008663 A125334
Adjacent sequences: A001699 A001700 A001701 this_sequence A001703 A001704 A001705
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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