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

Author

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

Keywords

• nonn

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.

Crossrefs

Cf. A003319, A141307.

Programs

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 *)

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