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
Vincenzo Librandi, Table of n, a(n) for n = 1..200
J. Riordan, Cached copy of paper
FORMULA
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from R. J. Mathar, Jul 15 2008
STATUS
approved