A316149 - OEIS

%I #15 Nov 21 2022 08:52:36

%S 2,-1,-1,2,-3,3,0,-4,6,-6,6,-1,-12,24,-29,23,9,-64,114,-132,81,78,

%T -333,577,-627,279,610,-1896,2979,-2911,672,4232,-10754,15576,-13515,

%U -591,28098,-61548,81664,-60408,-27030,180784,-351081,425892,-253838,-281760,1140396,-1995767,2195952,-930876

%N Inverse Euler transform of Thue-Morse sequence A001285.

%H Seiichi Manyama, <a href="/A316149/b316149.txt">Table of n, a(n) for n = 1..5000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EulerTransform.html">Euler Tranceform</a>

%F Product_{k>=1} (1-x^k)^(-a(k)) = 1 + Sum_{k>=1} A001285(k)*x^k.

%e (1-x)^(-2)*(1-x^2)*(1-x^3)*(1-x^4)^(-2)* ... = 1 + 2*x + 2*x^2 + x^3 + 2*x^4 + ... .

%p # The function EulerInvTransform is defined in A358451.

%p a := EulerInvTransform(A001285):

%p seq(a(n), n = 1..50); # _Peter Luschny_, Nov 21 2022

%Y Cf. A001285, A029878.

%K sign

%O 1,1

%A _Seiichi Manyama_, Jun 25 2018