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 A227293 G.f.: sqrt( Sum_{n>=0} 4^n*x^(n^2) ). 1

%I

%S 1,2,-2,4,-2,12,-36,104,-330,1068,-3356,10808,-35156,115192,-380744,

%T 1267152,-4242778,14285644,-48336684,164272984,-560515836,1919455464,

%U -6594719992,22725877680,-78531331524,272062125048,-944738639640,3287748182064,-11464667424744,40053463412080,-140178051713680,491396601445280

%N G.f.: sqrt( Sum_{n>=0} 4^n*x^(n^2) ).

%e G.f.: A(x) = 1 + 2*x - 2*x^2 + 4*x^3 - 2*x^4 + 12*x^5 - 36*x^6 + 104*x^7 - 330*x^8 + 1068*x^9 - 3356*x^10 + 10808*x^11 - 35156*x^12 +...

%e where

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

%o (PARI) {a(n)=polcoeff(sqrt(sum(k=0,n,4^k*x^(k^2))+x*O(x^n)),n)}

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

%K sign

%O 0,2

%A _Paul D. Hanna_, Jul 05 2013

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Last modified May 6 09:45 EDT 2021. Contains 343580 sequences. (Running on oeis4.)