A141308 Euler transform of A141307.

2, 7, 36, 283, 2898, 36169, 524976, 8659186, 159736316, 3257811334, 72797444280, 1769125982092, 46466434382032, 1311960028913384, 39633438764146568, 1275742281105759813, 43593785716301112538, 1576217593145774955007

Offset

1,1

Comments

Dimensions of the graded components of the domain of cocommutativity of the Hopf algebra of free quasi-symmetric functions of level 2.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..400

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.

Formula

a(n) ~ n! * 2^n * (1 - 1/n - 5/(4*n^2) - 21/(4*n^3) - 469/(16*n^4) - 3375/(16*n^5) - 118775/(64*n^6) - 1227535/(64*n^7) - 29026957/(128*n^8) - 385505947/(128*n^9) - 22698285665/(512*n^10)). - Vaclav Kotesovec, Aug 07 2015

Maple

EULER([seq(c(n), n=1..20)]); # where c(n) is A141307.

Mathematica

Clear[c]; c[0]=0; c[n_] := c[n] = n! - Sum[k!*c[n-k], {k, 1, n-1}]; Rest[CoefficientList[Series[Product[1/(1 - x^k)^(2^k * c[k]), {k, 1, 20}], {x, 0, 20}], x]] (* Vaclav Kotesovec, Aug 07 2015 *)

Crossrefs

Cf. A003319, A141307.

Sequence in context: A090352 A123549 A009704 * A185161 A012712 A012363

Adjacent sequences: A141305 A141306 A141307 * A141309 A141310 A141311

Keyword

nonn

Author

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

Status

approved