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Search: id:A162552
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| A162552 |
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L.g.f.: log( Sum_{n>=1} x^(n^2) ), the log of the characteristic function of the squares. |
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+0
4
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| 1, -1, 1, 3, -4, 5, -6, 3, 10, -16, 23, -27, 14, 6, -34, 83, -101, 86, -37, -72, 204, -309, 346, -243, -29, 454, -908, 1214, -1130, 470, 776, -2413, 3884, -4421, 3244, 162, -5438, 11285, -15352, 14688, -6887, -8640, 29241, -48353, 56270, -42850, 1834
(list; graph; listen)
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OFFSET
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1,4
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FORMULA
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L.g.f.: L(x) = Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=1} x^(n^2) ).
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EXAMPLE
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L.g.f.: L(x) = x - 1*x^2/2 + 1*x^3/3 + 3*x^4/4 - 4*x^5/5 + 5*x^6/6 -...
exp(L(x)) = 1 + x + x^4 + x^9 + x^16 + x^25 + x^36 +...+ x^(n^2) +...
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PROGRAM
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(PARI) {a(n)=local(Q=sum(m=0, sqrtint(n+1), x^(m^2))+x*O(x^n)); n*polcoeff(log(Q), n)}
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CROSSREFS
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Cf. A162553, A002129, A010052.
Sequence in context: A103606 A139794 A004484 this_sequence A133575 A104136 A159624
Adjacent sequences: A162549 A162550 A162551 this_sequence A162553 A162554 A162555
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 06 2009
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