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A161803
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G.f.: A(x) = exp( Sum_{n>=1} A162552(n) * 2*A006519(n) * x^n/n ).
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0
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1, 2, 0, -2, 6, 12, 0, -8, 24, 44, 0, -30, 54, 104, 0, -60, 238, 466, 0, -402, 924, 1892, 0, -1228, 3264, 6006, 0, -4052, 6688, 13052, 0, -7452, 16536, 32140, 0, -24828, 39660, 85744, 0, -53592, 114336, 212406, 0, -141090, 190754, 386956, 0, -216572, 136078
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A162552 forms the l.g.f. of log[ Sum_{n>=0} x^(n^2) ], while
2*A006519 forms the l.g.f. of binary partitions (A000123) and
A006519(n) is the highest power of 2 dividing n.
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EXAMPLE
| G.f.: 1 + 2*x - 2*x^3 + 6*x^4 + 12*x^5 - 8*x^7 + 24*x^8 + 44*x^9 +...
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PROG
| (PARI) {a(n)=local(SQ=sum(m=0, sqrtint(n+1), x^(m^2))+x*O(x^n), L=sum(m=1, n, 2*2^valuation(m, 2)*polcoeff(log(SQ), m)*x^m)+x*O(x^n)); polcoeff(exp(L), n)}
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CROSSREFS
| Cf. A161800, A162552.
Sequence in context: A094385 A156815 A175802 * A057980 A081081 A111111
Adjacent sequences: A161800 A161801 A161802 * A161804 A161805 A161806
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KEYWORD
| sign
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 19 2009
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