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G.f.: ( Sum_{n>=0} 8^n*x^(n^2) )^(1/2).
1

%I #7 Sep 29 2024 17:01:40

%S 1,4,-8,32,-128,768,-4608,28672,-184320,1212672,-8127488,55318528,

%T -381329408,2656845824,-18680250368,132373807104,-944459216896,

%U 6778991403008,-48915734839296,354636355665920,-2582006464118784,18870792427143168,-138396900373037056,1018196233480568832,-7512565092559355904

%N G.f.: ( Sum_{n>=0} 8^n*x^(n^2) )^(1/2).

%e G.f.: A(x) = 1 + 4*x - 8*x^2 + 32*x^3 - 128*x^4 + 768*x^5 - 4608*x^6 +...

%e where

%e A(x)^2 = 1 + 8*x + 8^2*x^4 + 8^3*x^9 + 8^4*x^16 + 8^5*x^25 + 8^6*x^36 +...

%o (PARI) {a(n)=polcoeff((sum(k=0,n,8^k*x^(k^2))+x*O(x^n))^(1/2),n)}

%o for(n=0,36,print1(a(n),", "))

%Y Cf. A227294.

%K sign

%O 0,2

%A _Paul D. Hanna_, Jul 05 2013