%I #9 Aug 31 2018 15:58:17

%S 0,0,0,1,1,2,3,7,14,33,74,180,438,1090,2741,6994,17966,46565,121440,

%T 318597,839953,2224486,5914248,15780662,42241422,113402369,305254039,

%U 823690961,2227640597,6037142355,16392945284,44592703836

%N DIK(b)-DIK[ 2 ](b)-b where b is A035082.

%H Andrew Howroyd, <a href="/A035083/b035083.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 BIK(p)={(1/(1-p) + (1+p)/subst(1-p, x, x^2))/2}

%o DIK(p,n)={(sum(d=1, n, eulerphi(d)/d*log(subst(1/(1+O(x*x^(n\d))-p), x, x^d))) + ((1+p)^2/(1-subst(p, x, x^2))-1)/2)/2}

%o EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

%o seq(n)={my(p=O(x)); for(n=1, n, p=x+x^2*Ser(EulerT(Vec(BIK(p)-1)-Vec(p)))); Vec(DIK(p, n) - p - (p^2 + subst(p, x, x^2))/2, -(n+1))} \\ _Andrew Howroyd_, Aug 31 2018

%Y Cf. A035082, A035084, A035085.

%K nonn

%O 0,6

%A _Christian G. Bower_, Nov 15 1998