A337299 Expansion of Product_{k>0} (1 - 2^(k-1)*x^k).

1, -1, -2, -2, -4, 0, -8, 16, 0, 64, 64, 384, 0, 1536, 1024, 3072, 2048, 16384, -8192, 49152, -32768, 32768, -65536, 262144, -1835008, 524288, -3145728, -6291456, -18874368, -4194304, -117440512, -16777216, -301989888, -469762048, -671088640, -805306368, -6710886400, 536870912

Offset: 0

Author

Seiichi Manyama, Aug 22 2020

Keywords

• sign

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1, g(n) = 2^(n-1).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Convolution inverse of A075900.

Cf. A266964, A304961.

Programs

Mathematica

m = 37; CoefficientList[Series[Product[1 - 2^(k - 1)*x^k, {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, Aug 22 2020 *)

PARI

N=40; x='x+O('x^N); Vec(prod(k=1, N, 1-2^(k-1)*x^k))