%I #8 Sep 21 2018 02:20:49
%S 1,1,2,5,8,16,29,59,124,287,670,1634,3992,9867,24320,60290,149124,
%T 370146,918796,2286685,5697484,14227797,35583724,89168380,223794690,
%U 562624780,1416520302,3571567951,9017077418,22794093212
%N "DHK" (bracelet, identity, unlabeled) transform of 1,2,3,4,...
%H Andrew Howroyd, <a href="/A032254/b032254.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)^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