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A094362
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Expansion of (eta(q^3)eta(q^13))/(eta(q)eta(q^39)) in powers of q.
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0
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1, 1, 2, 2, 4, 5, 7, 9, 13, 16, 22, 27, 36, 43, 56, 68, 87, 104, 130, 156, 193, 230, 281, 333, 404, 477, 572, 673, 802, 940, 1113, 1299, 1531, 1780, 2085, 2418, 2820, 3259, 3784, 4362, 5047, 5799, 6685, 7662, 8806, 10066, 11532, 13152, 15026, 17098, 19482
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,3
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COMMENTS
| Euler transform of period 39 sequence [1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,...].
G.f. A(x) satisfies 0=f(A(x),A(x^2))=f(1/A(x),1/A(x^2)) where f(u,v)=u^3+v^3+2uv(u+v)-u^2v^2-uv.
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FORMULA
| G.f.: x^-1 Product_{k>0} (1-x^(3k))(1-x^(13k))/((1-x^k)(1-x^(39k))).
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PROG
| (PARI) a(n)=local(A); if(n<-1, 0, n++; A=x*O(x^n); polcoeff(eta(x^3+A)*eta(x^13+A)/eta(x+A)/eta(x^39+A), n))
(PARI) a(n)=local(A, u, v); if(n<0, 0, A=1/x; for(k=2, n, u=A+x*O(x^k); v=subst(u, x, x^2); A-=x^k*polcoeff(u^3+v^3+2*u*v*(u+v)-u^2*v^2-u*v, k+2)/2); polcoeff(A, n))
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CROSSREFS
| Cf. A058661. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 15 2008]
Sequence in context: A007209 A166239 A058661 * A000726 A128663 A174068
Adjacent sequences: A094359 A094360 A094361 * A094363 A094364 A094365
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, May 03 2004
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