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Search: id:A005002
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| A005002 |
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Number of rhyme schemes (see reference for precise definition).
(Formerly M3465)
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+0
3
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| 1, 4, 13, 41, 134, 471, 1819, 7778, 36703, 189381, 1057332, 6328261, 40300959, 271501240, 1925961025, 14332064197, 111528998198, 905134802555, 7643011810167, 67010181855706, 608890179868163, 5724496098183649
(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).
J. Riordan, A budget of rhyme scheme counts, pp. 455 - 465 of Second International Conference on Combinatorial Mathematics, New York, April 4-7, 1978. Edited by Allan Gewirtz and Louis V. Quintas. Annals New York Academy of Sciences, 319, 1979.
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LINKS
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J. Riordan, Cached copy of paper
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FORMULA
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a(k)=1. a(n)=k*a(n-1)+A000110(n-1)-A102661(n-1,k-2), k=2. - R. J. Mathar, Jul 15 2008
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MAPLE
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(Maple program from R. J. Mathar): A000110 := proc(n) combinat[bell](n) ; end:
A005001:=n->if n = 0 then 0; else add(combinat[bell](k), k=0..n); fi;
A102661 := proc(n, k) add(combinat[stirling2](n, i), i=1..k) ; end:
beta := proc(n, k) if k= 1 then A005001(n) ; elif k= n then 1 ; else k*beta(n-1, k)+A000110(n-1)-A102661(n-1, k-2) ; fi ; end:
A005002 := proc(n) beta(n, 2) ; end:
seq(A005002(n), n=2..30) ;
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CROSSREFS
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Cf. A005000, A005003, A127021.
Sequence in context: A049222 A001453 A141364 this_sequence A085507 A121654 A036366
Adjacent sequences: A004999 A005000 A005001 this_sequence A005003 A005004 A005005
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from R. J. Mathar, Jul 15 2008
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