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A141308 Euler transform of A141307. 2

%I

%S 2,7,36,283,2898,36169,524976,8659186,159736316,3257811334,

%T 72797444280,1769125982092,46466434382032,1311960028913384,

%U 39633438764146568,1275742281105759813,43593785716301112538,1576217593145774955007

%N Euler transform of A141307.

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

%H Vaclav Kotesovec, <a href="/A141308/b141308.txt">Table of n, a(n) for n = 1..400</a>

%H J.-C. Novelli and J.-Y. Thibon, <a href="https://arxiv.org/abs/0806.3682">Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions</a>, arXiv:0806.3682 [math.CO], 2008.

%F 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

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

%t 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 *)

%Y Cf. A003319, A141307.

%K nonn

%O 1,1

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

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Last modified January 23 15:59 EST 2022. Contains 350514 sequences. (Running on oeis4.)