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A164617
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Expansion of (phi^3(q^3) / phi(q)) * (psi(-q^3) / psi^3(-q)) in powers of q where phi(), psi() are Ramanujan theta functions.
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3
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1, 1, 4, 10, 20, 39, 76, 140, 244, 415, 696, 1140, 1820, 2861, 4448, 6816, 10292, 15372, 22756, 33356, 48408, 69683, 99600, 141312, 199036, 278557, 387608, 536230, 737632, 1009464, 1374888, 1863764, 2514868, 3378948, 4521672, 6027000, 8002676
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| Expansion of eta(q^6)^14 / (eta(q) * eta(q^2)^2 * eta(q^3)^5 * eta(q^4) * eta(q^12)^5) in powers of q.
Euler transform of period 12 sequence [ 1, 3, 6, 4, 1, -6, 1, 4, 6, 3, 1, 0, ...].
Convolution of A113973 and A132974. A164616(3*n) = a(n).
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EXAMPLE
| 1 + q + 4*q^2 + 10*q^3 + 20*q^4 + 39*q^5 + 76*q^6 + 140*q^7 + 244*q^8 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^6 + A)^14 / (eta(x + A) * eta(x^2 + A)^2 * eta(x^3 + A)^5 * eta(x^4 + A) * eta(x^12 + A)^5), n))}
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CROSSREFS
| Sequence in context: A090164 A128640 A128641 * A038421 A049032 A100354
Adjacent sequences: A164614 A164615 A164616 * A164618 A164619 A164620
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Aug 17 2009
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