A306159 Inverse Weigh transform of 5^n.

5, 15, 40, 165, 624, 2620, 11160, 48915, 217000, 976872, 4438920, 20346320, 93900240, 435970980, 2034504992, 9536767665, 44878791360, 211927733500, 1003867701480, 4768372070592, 22706531339280, 108372083629260, 518301258916440, 2483526875798820

Offset: 1

Author

Seiichi Manyama, Jun 23 2018

Keywords

• nonn

Examples

			(1+x)^5*(1+x^2)^15*(1+x^3)^40*(1+x^4)^165* ... = 1 + 5*x + 25*x^2 + 125*x^3 + 625*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), A306158 (b=4), this sequence (b=5).

Cf. A000351, A038070.

Formula

Product_{k>=1} (1+x^k)^a(k) = 1/(1-5x).

a(n) = (1/n) * (5^n + Sum_{d

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