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A227312
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L.g.f.: log(1 + 2*Sum_{n>=1} 2^n * x^(n^2)).
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2
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4, -16, 64, -224, 864, -3328, 12800, -49408, 190864, -736896, 2845440, -10987520, 42426752, -163825664, 632592384, -2442673664, 9432071040, -36420732160, 140633977856, -543040041984, 2096879372288, -8096830353408, 31264870391808, -120725281128448, 466165166208064, -1800036911561216, 6950611323771904
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OFFSET
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1,1
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COMMENTS
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Compare to the logarithm of theta_3(x) = 1 + 2*Sum_{n>=1} x^(n^2)):
log(theta_3(x)) = Sum_{n>=1} -(sigma(2*n) - sigma(n))*(-x)^n/n, where sigma is the sum of divisors of n (A000203).
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LINKS
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EXAMPLE
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L.g.f.: L(x) = 4*x - 16*x^2/2 + 64*x^3/3 - 224*x^4/4 + 864*x^5/5 - 3328*x^6/6 + 12800*x^7/7 - 49408*x^8/8 + 190864*x^9/9 - 736896*x^10/10 + 2845440*x^11/11 - 10987520*x^12/12 + 42426752*x^13/13 - 163825664*x^14/14 + 632592384*x^15/15 - 2442673664*x^16/16 +...
where
exp(L(x)) = 1 + 4*x + 8*x^4 + 16*x^9 + 32*x^16 + 64*x^25 + 128*x^36 + 256*x^49 +...
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PROG
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(PARI) {a(n)=n*polcoeff(log(1+sum(k=1, n, 2*2^k*x^(k^2))+x*O(x^n)), n)}
for(n=1, 36, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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