cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A141308 Euler transform of A141307.

This page as a plain text file.
%I A141308 #11 Nov 06 2016 04:41:54
%S A141308 2,7,36,283,2898,36169,524976,8659186,159736316,3257811334,
%T A141308 72797444280,1769125982092,46466434382032,1311960028913384,
%U A141308 39633438764146568,1275742281105759813,43593785716301112538,1576217593145774955007
%N A141308 Euler transform of A141307.
%C A141308 Dimensions of the graded components of the domain of cocommutativity of the Hopf algebra of free quasi-symmetric functions of level 2.
%H A141308 Vaclav Kotesovec, <a href="/A141308/b141308.txt">Table of n, a(n) for n = 1..400</a>
%H A141308 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 A141308 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 A141308 EULER([seq(c(n),n=1..20)]); # where c(n) is A141307.
%t A141308 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 A141308 Cf. A003319, A141307.
%K A141308 nonn
%O A141308 1,1
%A A141308 Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008