A352402 Expansion of Product_{k>=1} 1 / (1 + 2^(k-1)*x^k).

1, -1, -1, -3, -1, -7, -1, -15, 31, -63, 159, -95, 671, -287, 3231, -2975, 15519, -7839, 44191, -34975, 224415, -291999, 863391, -990367, 2927775, -4902047, 12561567, -27225247, 56470687, -102640799, 152153247, -422620319, 877243551, -2278272159, 3357125791

Offset

0,4

Links

Table of n, a(n) for n=0..34.

Formula

a(n) = Sum_{k=0..n} (-1)^k * p(n,k) * 2^(n-k), where p(n,k) is the number of partitions of n into k parts.

Mathematica

nmax = 34; CoefficientList[Series[Product[1/(1 + 2^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Table[Sum[(-1)^k Length[IntegerPartitions[n, {k}]] 2^(n - k), {k, 0, n}], {n, 0, 34}]

Crossrefs

Cf. A032302, A070877, A070933, A071109, A075900, A304961, A327550, A337299, A352762.

Sequence in context: A353961 A290678 A290422 * A278954 A350802 A331884

Adjacent sequences: A352399 A352400 A352401 * A352403 A352404 A352405

Keyword

sign

Author

Ilya Gutkovskiy, Jun 08 2022

Status

approved