%I #8 Sep 21 2018 02:20:43
%S 1,1,3,8,15,34,70,162,388,1020,2729,7580,21112,59398,166990,471635,
%T 1332492,3776712,10721570,30518960,87046334,248852142,712831894,
%U 2045974474,5882821341,16943916873,48878646537,141209193981
%N "DHK" (bracelet, identity, unlabeled) transform of 1,3,5,7,...
%H Andrew Howroyd, <a href="/A032255/b032255.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(x*(1+x)/(1-x)^2 + O(x*x^n), n))} \\ _Andrew Howroyd_, Sep 21 2018
%K nonn
%O 0,3
%A _Christian G. Bower_
%E a(0)=1 prepended by _Andrew Howroyd_, Sep 21 2018