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A001939
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Expansion of (psi(-x) / phi(-x))^5 in powers of x where phi(), psi() are Ramanujan theta functions.
(Formerly M3898 N1599)
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3
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1, 5, 20, 65, 185, 481, 1165, 2665, 5820, 12220, 24802, 48880, 93865, 176125, 323685, 583798, 1035060, 1806600, 3108085, 5276305, 8846884, 14663645, 24044285, 39029560, 62755345, 100004806, 158022900, 247710570, 385366265, 595212280
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
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REFERENCES
| A. Cayley, A memoir on the transformation of elliptic functions, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 9, p. 128.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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 q^(-5/8) * (eta(q^4) / eta(q))^5 in powers of q. - Michael Somos, Sep 24 2011
Euler transform of period 4 sequence [ 5, 5, 5, 0, ...]. - Michael Somos, Sep 24 2011
G.f.: (Product_{k>0} (1 - x^(4*k)) / (1 - x^k))^5. - Michael Somos, Sep 24 2011
a(n) = (-1)^n * A195861(n). - Michael Somos, Sep 24 2011
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EXAMPLE
| 1 + 5*x + 20*x^2 + 65*x^3 + 185*x^4 + 481*x^5 + 1165*x^6 + 2665*x^7 + ...
q^5 + 5*q^13 + 20*q^21 + 65*q^29 + 185*q^37 + 481*q^45 + 1165*q^53 + ...
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MATHEMATICA
| a[ n_] := SeriesCoefficient[ (EllipticTheta[ 2, 0, q] / EllipticTheta[ 2, Pi/4, q^(1/2)] / (16 q)^(1/8))^5, {q, 0, n}] (* Michael Somos, Sep 24 2011 *)
a[ n_] := SeriesCoefficient[ (Product[1 - x^k, {k, 4, n, 4}] / Product[1 - x^k, {k, n}])^5, {x, 0, n}] (* Michael Somos, Sep 24 2011 *)
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^4 + A) / eta(x + A))^5, n))} /* Michael Somos, Sep 24 2011 */
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CROSSREFS
| Cf. A195861.
Sequence in context: A011854 A203849 A195861 * A100534 A160506 A160528
Adjacent sequences: A001936 A001937 A001938 * A001940 A001941 A001942
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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