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A329156
Expansion of Product_{k>=1} 1 / (1 - Sum_{j>=1} j * x^(k*j)).
2
1, 1, 4, 10, 29, 72, 200, 510, 1364, 3546, 9348, 24400, 64090, 167562, 439200, 1149360, 3010349, 7879832, 20633304, 54014950, 141422328, 370239300, 969323000, 2537696160, 6643839400, 17393731933, 45537549048, 119218684970, 312119004990, 817137724392, 2139295489200, 5600747143950
OFFSET
0,3
COMMENTS
Euler transform of A032198.
FORMULA
G.f.: Product_{k>=1} 1 / (1 - x^k / (1 - x^k)^2).
G.f.: exp(Sum_{k>=1} ( Sum_{d|k} 1 / (d * (1 - x^(k/d))^(2*d)) ) * x^k).
G.f.: Product_{k>=1} 1 / (1 - x^k)^A032198(k).
G.f.: A(x) = Product_{k>=1} B(x^k), where B(x) = g.f. of A088305.
a(n) ~ phi^(2*n-1), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Nov 07 2019
MATHEMATICA
nmax = 31; CoefficientList[Series[Product[1/(1 - Sum[j x^(k j), {j, 1, nmax}]), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 31; CoefficientList[Series[Product[1/(1 - x^k/(1 - x^k)^2), {k, 1, nmax}], {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 06 2019
STATUS
approved