A321088 G.f. satisfies: A(x) = 1/(1 - x) * Product_{k>0} A(x^(2*k)) / Product_{k>1} A(x^(2*k-1)).

1, 1, 2, 1, 4, 2, 4, -1, 9, 3, 11, -4, 17, -2, 11, -24, 31, -3, 39, -35, 70, -14, 47, -107, 112, -27, 122, -163, 198, -90, 93, -409, 282, -108, 329, -487, 601, -160, 324, -1076, 835, -165, 907, -1298, 1478, -429, 565, -2973, 1745, -427, 1999, -3149, 3587, -528

Offset: 0

Author

Seiichi Manyama, Nov 05 2018

Keywords

• sign
• look

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• N. J. A. Sloane, Transforms

Crossrefs

Convolution inverse of A321326.

Cf. A067856, A073709, A129374.

Programs

Mathematica

b[n_] := If[n == 1, 1, Product[{p, e} = pe; If[2 == p, e--, If[e > 1, p = 0, p = -1]]; p^e, {pe, FactorInteger[n]}]];
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n - j], {j, 1, n}]/n]; b];
a = etr[b];
a /@ Range[0, 100] (* Jean-François Alcover, Oct 01 2019 *)

Formula

Euler transform of A067856.

G.f.: Product_{k>0} 1/(1 - x^k)^A067856(k).

Product_{k>0} A(x^k) = Product_{k>=0} 1/(1 - x^(2^k))^(2^k). (Cf. A073709.)