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Search: id:A006353
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| A006353 |
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Expansion of (eta(q^2)*eta(q^3))^7/(eta(q)*eta(q^6))^5 in powers of q.
(Formerly M3825)
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+0
1
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| 1, 5, 13, 23, 29, 30, 31, 40, 61, 77, 78, 60, 47, 70, 104, 138, 125, 90, 85, 100, 174, 184, 156, 120, 79, 155, 182, 239, 232, 150, 186, 160, 253, 276, 234, 240, 101, 190, 260, 322, 366, 210, 248, 220, 348, 462, 312, 240, 143, 285, 403, 414, 406, 270
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Expansion of a modular form related to Apery numbers A005259.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Beukers, F.; Another congruence for the Apery numbers. J. Number Theory 25 (1987), no. 2, 201-210.
M. Kontsevich and D. Zagier, Periods, pp. 771-808 of B. Engquist and W. Schmid, editors, Mathematics Unlimited - 2001 and Beyond, 2 vols., Springer-Verlag, 2001.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
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Expansion of (phi(-q^3)psi(q))^3/(phi(-q)psi(q^3)) in powers of q where phi(),psi() are Ramanujan theta functions.
Expansion of (b(q^2)^2/b(q))(c(q)^2/c(q^2))/3 in powers of q where b(),c() are cubic AGM analog functions.
Euler transform of period 6 sequence [ 5, -2, -2, -2, 5, -4, ...]. - Michael Somos Oct 11 2006
G.f.: Product_{k>0} (1-x^k)^2*(1-x^(3k))^2*(1+x^k)^7/(1+x^(3k))^5.
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PROGRAM
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(PARI) {a(n)=if(n<1, n==0, sumdiv(n, d, d*[0, 5, 4, 6, 4, 5][d%6+1]))} /* Michael Somos Oct 11 2006 */
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)*eta(x^3+A))^7/(eta(x+A)*eta(x^6+A))^5, n))} /* Michael Somos Oct 11 2006 */
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CROSSREFS
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Sequence in context: A060004 A076408 A083800 this_sequence A155142 A155552 A143988
Adjacent sequences: A006350 A006351 A006352 this_sequence A006354 A006355 A006356
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Extended with PARI programs by Michael Somos
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