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A005003
Number of rhyme schemes (see reference for precise definition).
(Formerly M4416)
3
1, 7, 35, 156, 670, 2886, 12797, 59537, 294585, 1562324, 8900568, 54346140, 353937741, 2444771767, 17814457447, 136308242144, 1091001532590, 9105746802826, 79041398643849, 711994012088297, 6642697774712213
OFFSET
1,2
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).
LINKS
FORMULA
a(k)=1. a(n)=k*a(n-1)+A000110(n-1)-A102661(n-1,k-2), k=3. - R. J. Mathar, Jul 15 2008
MAPLE
(Maple program from R. J. Mathar):
A000110 := proc(n) combinat[bell](n) ; end:
A102661 := proc(n, k) add(combinat[stirling2](n, i), i=1..k) ; end:
A005001:=n->if n = 0 then 0; else add(combinat[bell](k), k=0..n); fi;
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:
A005003 := proc(n) beta(n, 3) ; end:
seq(A005003(n), n=3..30) ;
MATHEMATICA
a[1] = 1; a[n_] := 3*a[n-1] + BellB[n+1] - StirlingS2[n+1, 1]; a /@ Range[21] (* Jean-François Alcover, May 20 2011, after R. J. Mathar *)
CROSSREFS
Sequence in context: A006095 A171477 A265612 * A243382 A242577 A163348
KEYWORD
nonn
EXTENSIONS
More terms from R. J. Mathar, Jul 15 2008
STATUS
approved