|
Search: id:A134988
|
|
|
| A134988 |
|
Number of formal expessions obtained by applying iterated binary brackets to n indexed symbols x_1, ...,x_n such that: 1) each symbol appears exactly once; 2) the smallest index inside a bracket appears on the left hand side and the largest index appears on the right hand side; 3) the outer bracket is the only bracket such that its set of indices is a sequence of consecutive integers. |
|
+0
1
|
|
| 1, 0, 1, 4, 22, 144, 1089, 9308, 88562, 927584, 10603178, 131368648, 1753970380, 25112732512, 383925637137, 6243618722124, 107644162715098, 1961478594977856, 37671587406585006
(list; graph; listen)
|
|
|
OFFSET
|
2,4
|
|
|
COMMENT
|
a(n) = number of generators in arity n of the operad Lie, when considered as a free non-symmetric operad.
a(n) = (1/e)*(1-3/n-5/(2n^2)+O(1/n^3))
|
|
LINKS
|
P. Salvatore and R. Tauraso, The Operad Lie is Free, arXiv:math.QA/0802.3010.
|
|
FORMULA
|
a(2)=1, a(n)=sum_{k=2..n-2}((k+1)*a(k+1)+a(k))*a(n-k), n>2; G.f.: A(x)=x-series_reversion(x*F(x)); where F(x) is the g.f. of the factorials (A000142).
|
|
CROSSREFS
|
Cf. A075834.
Sequence in context: A045744 A104991 A027391 this_sequence A081002 A057834 A121394
Adjacent sequences: A134985 A134986 A134987 this_sequence A134989 A134990 A134991
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paolo Salvatore and Roberto Tauraso (tauraso(AT)axp.mat.uniroma2.it), Feb 05 2008, Feb 22 2008
|
|
|
Search completed in 0.002 seconds
|
