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

1,1

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

Formula

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

a(n) = 1/n*(5^n + Sum_{d<n and d|n} (-1)^(n/d)*d*a(d)).

Example

(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 + ... .

Crossrefs

Inverse Weigh transform of b^n: A306156 (b=2), A306157 (b=3), A306158 (b=4), this sequence (b=5).

Cf. A000351, A038070.

Sequence in context: A301980 A230955 A038066 * A113861 A337207 A080870

Adjacent sequences: A306156 A306157 A306158 * A306160 A306161 A306162

Keyword

nonn

Author

Seiichi Manyama, Jun 23 2018

Status

approved