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A005002
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Number of rhyme schemes (see reference for precise definition).
(Formerly M3465)
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| J. Riordan, Cached copy of paper
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FORMULA
| 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
| (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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MATHEMATICA
| a[1]=1; a[n_] := a[n] = 2a[n-1] + BellB[n]; a /@ Range[22]
(* From Jean-François Alcover, May 19 2011, after R. J. Mathar *)
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CROSSREFS
| Cf. A005000, A005003, A127021.
Sequence in context: A049222 A001453 A141364 * A085507 A121654 A186202
Adjacent sequences: A004999 A005000 A005001 * A005003 A005004 A005005
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from R. J. Mathar, Jul 15 2008
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