A300152 - OEIS

%I #8 Aug 20 2018 09:29:10

%S 1,1,4,204,21365,3655450,914720443,314376587287,142230235674161,

%T 82054323238595173,58859164893105387442,51422171965089961951920,

%U 53779967726784762649882252,66358210285736859276931328215,95403541500521180624070289201028,158111431872131942988858401878995245,299245447906369767603866411915527014775

%N G.f. A(x) satisfies: 1 = Sum_{n>=0} ( (1+x)^(n^2) - A(x)^n )^n.

%e G.f.: A(x) = 1 + x + 4*x^2 + 204*x^3 + 21365*x^4 + 3655450*x^5 + 914720443*x^6 + 314376587287*x^7 + 142230235674161*x^8 + 82054323238595173*x^9 + ...

%e such that

%e 1 = 1 + ((1+x) - A(x)) + ((1+x)^4 - A(x)^2)^2 + ((1+x)^9 - A(x)^3)^3 + ((1+x)^16 - A(x)^4)^4 + ((1+x)^25 - A(x)^5)^5 + ((1+x)^36 - A(x)^6)^6 + ...

%o (PARI) {a(n) = my(A=[1]); for(i=1,n, A=concat(A,0); A[#A] = Vec( sum(m=0,#A, ((1+x +x*O(x^#A))^(m^2) - Ser(A)^m)^m ) )[#A] ); A[n+1]}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A304639.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 30 2018