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A212907
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Expansion of x^(-1/3) * psi(x^3) * c(x) / 3 in powers of x where psi() is a Ramanujan theta function and c() is a cubic AGM theta function.
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1
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1, 1, 2, 1, 3, 3, 2, 2, 2, 5, 3, 3, 4, 4, 3, 4, 3, 5, 3, 6, 6, 3, 4, 5, 5, 7, 5, 4, 4, 4, 8, 3, 6, 7, 9, 7, 5, 4, 3, 9, 7, 4, 7, 5, 10, 5, 8, 8, 4, 7, 9, 6, 8, 7, 8, 10, 5, 6, 5, 9, 10, 7, 8, 6, 7, 10, 7, 12, 6, 10, 7, 5, 12, 6, 12, 14, 6, 6, 5, 11, 6, 8, 10
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OFFSET
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0,3
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COMMENTS
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Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
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LINKS
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Table of n, a(n) for n=0..82.
M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
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Expansion of q^(-17/24) * eta(q^3)^2 * eta(q^6)^2 / eta(q) in powers of q.
Euler transform of period 6 sequence [ 1, 1, -1, 1, 1, -3, ...].
G.f.: Product_{k>0} (1 - x^(3*k))^2 * (1 - x^(6*k))^2 / (1 - x^k).
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EXAMPLE
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1 + x + 2*x^2 + x^3 + 3*x^4 + 3*x^5 + 2*x^6 + 2*x^7 + 2*x^8 + 5*x^9 + ...
q^17 + q^41 + 2*q^65 + q^89 + 3*q^113 + 3*q^137 + 2*q^161 + 2*q^185 + ...
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PROG
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^2 * eta(x^6 + A)^2 / eta(x + A), n))}
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CROSSREFS
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Sequence in context: A179480 A035050 A198790 * A046819 A159945 A089216
Adjacent sequences: A212904 A212905 A212906 * A212908 A212909 A212910
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jun 16 2012
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STATUS
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approved
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