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
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) ; # R. J. Mathar, Jul 15 2008
MATHEMATICA
a[1]=1; a[n_] := a[n] = 2a[n-1] + BellB[n]; a /@ Range[22]
(* Jean-François Alcover, May 19 2011, after R. J. Mathar *)
nxt[{n_, a_}]:={n+1, 2a+BellB[n+1]}; Transpose[NestList[nxt, {1, 1}, 30]] [[2]] (* Harvey P. Dale, Apr 20 2015 *)
PROG
(Haskell)
a005002 n = a005002_list !! (n-1)
a005002_list = 1 : zipWith (+) (map (* 2) a005002_list)
(drop 2 a000110_list)
-- Reinhard Zumkeller, Jun 19 2015
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from R. J. Mathar, Jul 15 2008
STATUS
approved