A357380 -id:A357380 - cp's OEIS frontend

A357381 Expansion of Product_{k>=1} 1 / (1 + x^Fibonacci(k)).

1, -2, 2, -3, 5, -7, 9, -11, 13, -16, 20, -23, 26, -31, 36, -41, 48, -55, 62, -71, 81, -92, 104, -116, 129, -145, 163, -180, 198, -219, 242, -267, 293, -320, 349, -381, 416, -452, 489, -529, 572, -618, 668, -719, 771, -829, 892, -956, 1023, -1094, 1167, -1246, 1331, -1416, 1504

Offset: 0

Ilya Gutkovskiy, Sep 26 2022

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Convolution inverse of A000121.

Cf. A000045, A000121, A298949, A357380.

nmax = 54; CoefficientList[Series[Product[1/(1 + x^Fibonacci[k]), {k, 1, 21}], {x, 0, nmax}], x]

A357520 Expansion of Product_{k>=0} (1 - x^Lucas(k)).

Original entry on oeis.org

1, -1, -1, 0, 0, 2, 0, -1, 0, 0, 1, -1, -1, 1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 0, 0, 1, -1, -1, 0, 0, 2, 0, 0, -1, -1, 1, 0, 0, 0, 0, 1, -1, -1, 0, 0, 2, 0, -1, 0, 0, 1, 0, -2, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 2, 0, -1, 0, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 0, -1, 0, 2, 0, 0, -1, -1, 1

Offset: 0

Ilya Gutkovskiy, Oct 02 2022

sign

Convolution inverse of A067593.

Cf. A000032, A067593, A093996, A357380, A357382.

nmax = 100; CoefficientList[Series[Product[(1 - x^LucasL[k]), {k, 0, 20}], {x, 0, nmax}], x]

cp's OEIS Frontend

A357381 Expansion of Product_{k>=1} 1 / (1 + x^Fibonacci(k)).

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