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A255319
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Expansion of psi(x^3) * f(x, x^5) in powers of x where psi(), f() are Ramanujan theta functions.
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7
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1, 1, 0, 1, 1, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 2, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 3, 1
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OFFSET
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0,9
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COMMENTS
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LINKS
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FORMULA
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Expansion of chi(x) * f(-x^6) * f(-x^12) in powers of x where chi(), f() are Ramanujan theta functions.
Expansion of q^(-17/24) * eta(q^2)^2 * eta(q^6) * eta(q^12) / (eta(q) * eta(q^4)) in powers of q.
Euler transform of period 12 sequence [ 1, -1, 1, 0, 1, -2, 1, 0, 1, -1, 1, -2, ...].
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EXAMPLE
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G.f. = 1 + x + x^3 + x^4 + x^5 + 2*x^8 + x^9 + x^10 + x^11 + x^14 + x^16 + ...
G.f. = q^17 + q^41 + q^89 + q^113 + q^137 + 2*q^209 + q^233 + q^257 + q^281 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x^6] QPochhammer[ x^12] QPochhammer[ -x, x^2], {x, 0, n}];
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PROG
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(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^6 + A) * eta(x^12 + A) / (eta(x + A) * eta(x^4 + A)), n))};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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