A309044 Expansion of Product_{k>=0} (1 + x^(2^k) - x^(2^(k+1)))^2.

1, 2, 1, 2, 0, -2, 3, 2, -1, -4, 0, -4, 5, 10, -3, -2, 0, -6, -1, -6, 3, 8, -8, -8, 9, 18, 1, 10, -8, -26, 11, 2, -1, 4, -8, -12, 5, 10, -11, -10, 8, 18, -1, 10, -13, -32, 8, 0, 9, 34, 1, 18, -8, -34, 27, 18, -17, -36, -8, -36, 29, 74, -35, -18, 8, -6, 7, 10, -13, -24

Offset

0,2

Links

Table of n, a(n) for n=0..69.

Formula

G.f. A(x) satisfies: A(x) = (1 + x - x^2)^2 * A(x^2).

a(n) = Sum_{k=0..n} A005590(k+1)*A005590(n-k+1).

Mathematica

nmax = 69; CoefficientList[Series[Product[(1 + x^(2^k) - x^(2^(k + 1)))^2, {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
nmax = 69; A[_] = 1; Do[A[x_] = (1 + x - x^2)^2 A[x^2] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A002487, A005590, A309043.

Sequence in context: A144736 A137423 A127471 * A240312 A339898 A273163

Adjacent sequences: A309041 A309042 A309043 * A309045 A309046 A309047

Keyword

sign

Author

Ilya Gutkovskiy, Jul 09 2019

Status

approved