A032254 "DHK" (bracelet, identity, unlabeled) transform of 1,2,3,4,...

1, 1, 2, 5, 8, 16, 29, 59, 124, 287, 670, 1634, 3992, 9867, 24320, 60290, 149124, 370146, 918796, 2286685, 5697484, 14227797, 35583724, 89168380, 223794690, 562624780, 1416520302, 3571567951, 9017077418, 22794093212

Offset: 0

Author

Christian G. Bower

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• C. G. Bower, Transforms (2)

Programs

PARI

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}
seq(n)={Vec(1 + DHK(x/(1-x)^2 + O(x*x^n), n))} \\ Andrew Howroyd, Sep 21 2018

Extensions

a(0)=1 prepended by Andrew Howroyd, Sep 21 2018