A032245 - OEIS

%I #8 Sep 21 2018 02:21:08

%S 1,1,1,2,2,3,4,6,10,19,35,68,133,259,500,976,1868,3609,6911,13296,

%T 25456,48925,93786,180326,346432,667009,1284331,2477342,4781021,

%U 9240027,17870724,34604082,67058896,130085007,252545177,490722360

%N "DHK" (bracelet, identity, unlabeled) transform of 1,1,1,1,...

%H Andrew Howroyd, <a href="/A032245/b032245.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) + O(x*x^n), n))} \\ _Andrew Howroyd_, Sep 21 2018

%K nonn

%O 0,4

%A _Christian G. Bower_

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