login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A141309 INVERTi transform of A141308. 1
2, 3, 16, 158, 1796, 24250, 372656, 6429927, 122956714, 2581840735, 59084565968, 1464445686726, 39101805324620, 1119446453417490, 34220008384633264, 1112764183812405300, 38362648544330997488, 1397884269388233025156 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of generators of degree n of the (free) primitive Lie algebra of the Hopf algebra of free quasi-symmetric functions of level 2.

LINKS

Table of n, a(n) for n=1..18.

J.-C. Novelli and J.-Y. Thibon, Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions, arXiv:0806.3682 [math.CO], 2008.

MAPLE

INVERTi([seq(d(n, n=1..20)]); # where d(n) is A141308

MATHEMATICA

terms = 18;

c[0] = 0; c[n_] := c[n] = n! - Sum[k! c[n-k], {k, 1, n-1}];

s = (Product[1/(1-x^k)^(2^k c[k]), {k, 1, terms+1}] + O[x]^(terms+1)-1)/x;

CoefficientList[-1/(1 + x s) + O[x]^(terms+1), x] // Rest (* Jean-François Alcover, Feb 13 2019 *)

CROSSREFS

Cf. A003319, A141307, A141308.

Sequence in context: A063666 A006247 A052318 * A179442 A299424 A215638

Adjacent sequences:  A141306 A141307 A141308 * A141310 A141311 A141312

KEYWORD

nonn

AUTHOR

Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 10:54 EST 2021. Contains 349428 sequences. (Running on oeis4.)