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A111317
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Let qf(a,q) = Product(1-a*q^j,j=0..infinity); g.f. is qf(q^2,q^3)/qf(q,q^3).
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2
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1, 1, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, -1, 0, 2, -1, -1, 2, -1, -2, 3, 1, -3, 2, 1, -4, 2, 3, -4, 1, 4, -5, 0, 6, -5, -2, 7, -5, -4, 10, -3, -7, 10, -2, -10, 11, 1, -13, 11, 4, -16, 11, 9, -19, 8, 12, -22, 7, 19, -24, 2, 24, -26, -3, 32, -25, -10, 37, -25, -18, 45, -21, -29, 49, -17, -39, 56, -8, -51, 58, 0, -65, 61, 14, -78, 59, 27, -92
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,15
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REFERENCES
| G. E. Andrews and B. C. Berndt, Your Hit Parade: The Top Ten Most Fascinating Formulas in Ramanujan's Lost Notebook, Notices Amer. Math. Soc., 55 (No. 1, 2008), 18-30. See p. 25, Equation (39).
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FORMULA
| Euler transform of period 3 sequence [ 1, -1, 0, ...]. - Michael Somos Dec 23 2007
G.f.: Product_{k>=0} (1 - x^(3*k+2)) / (1 - x^(3*k+1)).
G.f.: exp( Sum_{n>=1} 1/(1 + x^n + x^(2n)) * x^n/n ). [From Paul D. Hanna (pauldhanna(AT)juno.com), Jan 23 2010]
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PROG
| (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=0, n\3, (1 - x^(3*k+2)) / (1 - x^(3*k+1)), 1 + x * O(x^n)), n))} /* Michael Somos Dec 23 2007 */
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, 1/(1+x^m+x^(2*m)+x*O(x^n))*x^m/m)), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Jan 23 2010]
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CROSSREFS
| Convolution inverse of A111165.
Sequence in context: A175190 A137900 A025837 * A105202 A099386 A161067
Adjacent sequences: A111314 A111315 A111316 * A111318 A111319 A111320
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 09 2005
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