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Search: id:A093068
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| A093068 |
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Expansion of (eta(q^3)^2eta(q^7)eta(q^63))/(eta(q)eta(q^9)eta(q^21)^2) in powers of q. |
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+0
1
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| 1, 1, 2, 1, 3, 3, 4, 3, 5, 6, 9, 8, 11, 12, 15, 16, 18, 21, 26, 28, 35, 39, 47, 51, 58, 66, 77, 85, 97, 108, 125, 141, 156, 174, 195, 218, 245, 270, 304, 336, 377, 417, 467, 512, 573, 627, 702, 770, 853, 935, 1035, 1136, 1257, 1371, 1515, 1654, 1822, 1989, 2184, 2382
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Euler transform of period 63 sequence [1,1,-1,1,1,-1,0,1,0,1,1,-1,1,0,-1,1,1,0,1,1,0,1,1,-1,1,1,0,0,1,-1,1,1,-1,1,0,0,1,1,-1,1,1,0,1,1,0,1,1,-1,0,1,-1,1,1,0,1,0,-1,1,1,-1,1,1,0,...].
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FORMULA
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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.
G.f.: x Product_{k>0} ((1-x^(3k))^2(1-x^(7k))(1-x^(63k))/(1-x^k)(1-x^(9k))(1-x^(21k))^2).
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PROGRAM
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(PARI) a(n)=local(A, u, v); if(n<0, 0, A=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))
(PARI) a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff(eta(x^3+A)^2*eta(x^7+A)*eta(x^63+A)/eta(x+A)/eta(x^9+A)/eta(x^21+A)^2, n))
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CROSSREFS
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Sequence in context: A116087 A163281 A116921 this_sequence A097357 A123621 A151662
Adjacent sequences: A093065 A093066 A093067 this_sequence A093069 A093070 A093071
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 17 2004
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