A032251 - OEIS

%I #9 Sep 21 2018 02:21:03

%S 1,2,3,6,9,18,45,118,336,954,2695,7590,21321,59890,168273,473966,

%T 1337476,3785154,10738373,30546502,87099571,248937978,712995733,

%U 2046236598,5883318437,16944709370,48880145967,141211579446

%N "DHK" (bracelet, identity, unlabeled) transform of 2,2,2,2,...

%H Andrew Howroyd, <a href="/A032251/b032251.txt">Table of n, a(n) for n = 0..500</a>

%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>

%o (PARI)

%o DHK(p,n)={my(q=((1+p)^2/(1-subst(p, x, x^2))-1)/2); p + (p^2-subst(p, x, x^2))/2 + sum(d=1, n, moebius(d)*(log(subst(1/(1+O(x*x^(n\d))-p), x, x^d))/d - subst(q + O(x*x^(n\d)), x, x^d)))/2}

%o seq(n)={Vec(1 + DHK(2*x/(1-x) + O(x*x^n), n))} \\ _Andrew Howroyd_, Sep 21 2018

%K nonn

%O 0,2

%A _Christian G. Bower_

%E a(0)=1 prepended by _Andrew Howroyd_, Sep 21 2018