A306158 Inverse Weigh transform of 4^n.

4, 10, 20, 70, 204, 690, 2340, 8230, 29120, 104958, 381300, 1398430, 5162220, 19175130, 71582716, 268439590, 1010580540, 3817763040, 14467258260, 54975633906, 209430785460, 799645010850, 3059510616420, 11728124726270, 45035996273664, 173215372864590

Offset: 1

Author

Seiichi Manyama, Jun 23 2018

Keywords

• nonn

Examples

			(1+x)^4*(1+x^2)^10*(1+x^3)^20*(1+x^4)^70* ... = 1 + 4*x + 16*x^2 + 64*x^3 + 256*x^4 + ... .
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• 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), A306157 (b=3), this sequence (b=4), A306159 (b=5).

Cf. A000302, A038069.

Formula

Product_{k>=1} (1+x^k)^a(k) = 1/(1-4x).

a(n) = (1/n) * (4^n + Sum_{d

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