A300414 - OEIS

%I #5 Mar 06 2018 17:50:34

%S 1,2,4,8,12,20,30,42,62,84,114,154,198,260,332,418,530,654,810,994,

%T 1202,1462,1752,2094,2500,2948,3486,4092,4776,5582,6468,7490,8650,

%U 9928,11406,13036,14862,16934,19196,21758,24592,27706,31216,35038,39284,43990,49100,54798,61008,67798

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

%C Convolution of the sequences A000119 and A003107.

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

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

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

%Y Cf. A000045, A000119, A003107, A015128, A080054, A103265, A280263, A280366, A300413, A300415.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Mar 05 2018