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G.f. A(x) satisfies: A(x) = Product_{k>=1} 1/(1 - x^k*A(x)^k)^k.
6

%I #6 Mar 21 2018 17:15:04

%S 1,1,4,16,74,360,1840,9698,52409,288697,1615275,9153850,52434770,

%T 303104532,1765920785,10358843904,61129390652,362650003202,

%U 2161590275029,12938838382316,77745063802045,468760264760369,2835272729215565,17198394229862818,104598950726341920,637709136315071504

%N G.f. A(x) satisfies: A(x) = Product_{k>=1} 1/(1 - x^k*A(x)^k)^k.

%F G.f. A(x) satisfies: A(x) = exp(Sum_{k>=1} sigma_2(k)*x^k*A(x)^k/k).

%e G.f. A(x) = 1 + x + 4*x^2 + 16*x^3 + 74*x^4 + 360*x^5 + 1840*x^6 + 9698*x^7 + 52409*x^8 + 288697*x^9 + ...

%e G.f. A(x) satisfies: A(x) = 1/((1 - x*A(x)) * (1 - x^2*A(x)^2)^2 * (1 - x^3*A(x)^3)^3 * ...).

%e log(A(x)) = x + 7*x^2/2 + 37*x^3/3 + 215*x^4/4 + 1251*x^5/5 + 7459*x^6/6 + 44885*x^7/7 + 272727*x^8/8 + ... + A255672(n)*x^n/n + ...

%Y Cf. A000219, A001157, A109085, A145268, A255672, A301456.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 21 2018