A306157 Inverse Weigh transform of 3^n.

3, 6, 8, 24, 48, 124, 312, 834, 2184, 5928, 16104, 44344, 122640, 341796, 956576, 2690844, 7596480, 21524412, 61171656, 174342192, 498111952, 1426419852, 4093181688, 11767919284, 33891544368, 97764131640, 282429535752, 817028472936, 2366564736720, 6863038212784

Offset: 1

Author

Seiichi Manyama, Jun 23 2018

Keywords

• nonn

Examples

			(1+x)^3*(1+x^2)^6*(1+x^3)^8*(1+x^4)^24* ... = 1 + 3*x + 9*x^2 + 27*x^3 + 81*x^4 + ... .
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..2000
• 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: A306156 (b=2), this sequence (b=3), A306158 (b=4), A306159 (b=5).

Cf. A000244, A038068.

Formula

Product_{k>=1} (1+x^k)^a(k) = 1/(1-3x).

a(n) = (1/n) * (3^n + Sum_{d

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