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A193234
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G.f.: A(x) = ( 1 + Sum_{n>=1} 2*(-2)^n * x^(n^2) )^(-1/2).
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1
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1, 2, 6, 20, 66, 228, 804, 2872, 10374, 37780, 138436, 509832, 1885396, 6996472, 26039592, 97160592, 363332534, 1361320284, 5109306148, 19205627608, 72292274076, 272454449560, 1027979651384, 3882579544656, 14677889406396, 55536827825096
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OFFSET
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0,2
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COMMENTS
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Compare the g.f. to the theta_3 series: 1 + Sum_{n>=1} 2*x^(n^2).
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LINKS
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EXAMPLE
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G.f.: A(x) = 1 + 2*x + 6*x^2 + 20*x^3 + 66*x^4 + 228*x^5 + 804*x^6 +...
where
1/A(x)^2 = 1 - 4*x + 8*x^4 - 16*x^9 + 32*x^16 - 64*x^25 + 128*x^36 - 256*x^49 + 512*x^64 +...+ 2*(-2)^n*x^(n^2) +...
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PROG
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(PARI) {a(n)=local(S=1+sum(m=1, sqrtint(n), 2*(-2)^m*x^(m^2))+x*O(x^n)); polcoeff(S^(-1/2), n)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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