A300414 - OEIS

A300414

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

1, 2, 4, 8, 12, 20, 30, 42, 62, 84, 114, 154, 198, 260, 332, 418, 530, 654, 810, 994, 1202, 1462, 1752, 2094, 2500, 2948, 3486, 4092, 4776, 5582, 6468, 7490, 8650, 9928, 11406, 13036, 14862, 16934, 19196, 21758, 24592, 27706, 31216, 35038, 39284, 43990, 49100, 54798, 61008, 67798

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OFFSET

0,2

COMMENTS

Convolution of the sequences A000119 and A003107.

LINKS

Table of n, a(n) for n=0..49.

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=2} (1 + x^A000045(k))/(1 - x^A000045(k)).

MATHEMATICA

nmax = 49; CoefficientList[Series[Product[(1 + x^Fibonacci[k])/(1 - x^Fibonacci[k]), {k, 2, 20}], {x, 0, nmax}], x]