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

Author

Seiichi Manyama, Jun 23 2018

Keywords

• nonn

Examples

			(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 + ... .
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..3000
• Christian G. Bower, PARI programs for transforms, 2007.
• N. J. A. Sloane, Maple programs for transforms, 2001-2020.

Crossrefs

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

Cf. A000079, A038067, A102866.

Formula

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

a(n) = (1/n) * (2^n + Sum_{d

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