A035083 DIK(b)-DIK[ 2 ](b)-b where b is A035082.

0, 0, 0, 1, 1, 2, 3, 7, 14, 33, 74, 180, 438, 1090, 2741, 6994, 17966, 46565, 121440, 318597, 839953, 2224486, 5914248, 15780662, 42241422, 113402369, 305254039, 823690961, 2227640597, 6037142355, 16392945284, 44592703836

Offset: 0

Author

Christian G. Bower, Nov 15 1998

Keywords

• nonn

Links

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

Crossrefs

Cf. A035082, A035084, A035085.

Programs

PARI

BIK(p)={(1/(1-p) + (1+p)/subst(1-p, x, x^2))/2}
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}
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
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