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A301456
G.f. A(x) satisfies: A(x) = Product_{k>=1} (1 + x^k*A(x)^k)^k.
7
1, 1, 3, 12, 49, 217, 1006, 4810, 23576, 117812, 597937, 3073874, 15972678, 83758809, 442681653, 2355678968, 12610759255, 67868269712, 366979432955, 1992755590086, 10862329206524, 59414599714958, 326009477088080, 1793977307978268, 9898072238695390, 54744525395860053, 303463833091357785
OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = exp(Sum_{k>=1} (-1)^(k+1)*x^k*A(x)^k/(k*(1 - x^k*A(x)^k)^2)).
EXAMPLE
G.f. A(x) = 1 + x + 3*x^2 + 12*x^3 + 49*x^4 + 217*x^5 + 1006*x^6 + 4810*x^7 + 23576*x^8 + 117812*x^9 + ...
G.f. A(x) satisfies: A(x) = (1 + x*A(x)) * (1 + x^2*A(x)^2)^2 * (1 + x^3*A(x)^3)^3 * (1 + x^4*A(x)^4)^4 * ...
log(A(x)) = x + 5*x^2/2 + 28*x^3/3 + 141*x^4/4 + 751*x^5/5 + 4064*x^6/6 + 22198*x^7/7 + 122381*x^8/8 + ... + A270922(n)*x^n/n + ...
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 21 2018
STATUS
approved