A306156 Inverse Weigh transform of 2^n.

2, 3, 2, 6, 6, 11, 18, 36, 56, 105, 186, 346, 630, 1179, 2182, 4116, 7710, 14588, 27594, 52482, 99858, 190743, 364722, 699216, 1342176, 2581425, 4971008, 9587574, 18512790, 35792449, 69273666, 134219796, 260300986, 505294125, 981706806, 1908881548, 3714566310

Offset

1,1

Links

Seiichi Manyama, Table of n, a(n) for n = 1..3000

N. J. A. Sloane, Transforms

Formula

Product_{k>=1} (1+x^k)^a(k) = 1/(1-2x).

a(n) = 1/n*(2^n + Sum_{d<n and d|n} (-1)^(n/d)*d*a(d)).

Example

(1+x)^2*(1+x^2)^3*(1+x^3)^2*(1+x^4)^6* ... = 1 + 2*x + 4*x^2 + 8*x^3 + 16*x^4 + ... .

Crossrefs

Inverse Weigh transform of b^n: this sequence (b=2), A306157 (b=3), A306158 (b=4), A306159 (b=5).

Cf. A000079, A038067, A102866.

Sequence in context: A077418 A005421 A348083 * A276125 A208611 A209582

Adjacent sequences: A306153 A306154 A306155 * A306157 A306158 A306159

Keyword

nonn

Author

Seiichi Manyama, Jun 23 2018

Status

approved