A276527 - OEIS

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A276527

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

1, -1, 1, -3, 5, -8, 12, -21, 37, -59, 92, -153, 256, -409, 654, -1073, 1754, -2824, 4552, -7394, 12010, -19406, 31337, -50782, 82306, -133072, 215152, -348346, 563939, -912217, 1475604, -2388075, 3864808, -6252750, 10115987, -16369340, 26488326, -42857128

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OFFSET

0,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ -p / (sqrt(5) * r^(n+1)), where r = -(sqrt(5)-1)/2 and p = Product_{n>1} 1/(1 + r^n - r^(2*n)) = 1.0964214808924344474065093...

MATHEMATICA

nmax = 50; CoefficientList[Series[1/Product[1+x^k-x^(2*k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A003105, A162891.

Cf. A000726, A109389, A263401.