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Search: id:A006709
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| A006709 |
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Expansion of a modular function.
(Formerly M0600)
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+0
1
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| 1, -2, -3, -4, 22, 30, -12, -128, -147, 132, 548, 516, -552, -1924, -1572, 1784, 5790, 4410, -5180, -15608, -11406, 13712, 39128, 27528, -33518, -92682, -63156, 77284, 208636, 139026, -170272, -449904, -294741, 360872, 936836, 604440, -739228, -1892636
(list; graph; listen)
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OFFSET
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-2,2
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REFERENCES
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Newman, Morris; Construction and application of a class of modular functions. II. Proc. London Math. Soc. (3) 9 1959 373-387. MR0107629 (21 #6354).
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FORMULA
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Expansion of (eta(q)eta(q^2))^2(eta(q^3)^10/eta(q^6)^14) in powers of q. - Michael Somos Sep 22 2005
Euler transform of period 6 sequence [ -2, -4, -12, -4, -2, 0, ...]. - Michael Somos Sep 22 2005
G.f.: (x^-2)(Product_{k>0} (1-x^k)^2*(1-x^(2k))^2*(1-x^(3k))^10/ (1-x^(6k))^14).
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EXAMPLE
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1/q^2 -2/q -3 -4*q +22*q^2 +30*q^3 -12*q^4 -128*q^5 +...
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PROGRAM
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(PARI) {a(n)=local(A); if (n<-2, 0, n+=2; A=x*O(x^n); polcoeff( eta(x+A)^2*eta(x^2+A)^2*eta(x^3+A)^10/eta(x^6+A)^14, n))} /* Michael Somos Sep 22 2005 */
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CROSSREFS
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Sequence in context: A069801 A019074 A019075 this_sequence A115884 A010345 A000336
Adjacent sequences: A006706 A006707 A006708 this_sequence A006710 A006711 A006712
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KEYWORD
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sign,easy
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AUTHOR
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njas
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