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A002510
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Expansion of a modular function for Gamma_0(15).
(Formerly M1825 N0725)
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1
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1, 1, 2, 8, 10, 24, 53, 74, 153, 280, 436, 793, 1322, 2085, 3510, 5648, 8796, 14042, 21921, 33490, 51796, 78843, 118108, 178029, 265225, 390852, 576946, 843694, 1224329, 1775450, 2556360, 3658111, 5224159, 7418887, 10481780, 14773012, 20723154, 28941023
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OFFSET
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6,3
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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.
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
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FORMULA
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Expansion of eta(q^15)^13 / (eta(q) * eta(q^3)^5 * eta(q^5)^7) in powers of q.
Expansion of (c(q^5)^2 / (3 * c(q)))^2 / (b(q) * b(q^5)) in powers of q where b(), c() are cubic AGM theta functions. - Michael Somos, Jun 10 2012
Euler transform of period 15 sequence [1, 1, 6, 1, 8, 6, 1, 1, 6, 8, 1, 6, 1, 1, 0, ...]. - Michael Somos, Nov 10 2005
a(n) ~ exp(4*Pi*sqrt(2*n/15)) / (2^(1/4) * 3^(17/4) * 5^(13/4) * n^(3/4)). - Vaclav Kotesovec, Apr 09 2018
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EXAMPLE
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q^6 + q^7 + 2*q^8 + 8*q^9 + 10*q^10 + 24*q^11 + 53*q^12 + 74*q^13 + 153*q^14 + ...
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MAPLE
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with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: aa:=etr(n-> [1, 1, 6, 1, 8, 6, 1, 1, 6, 8, 1, 6, 1, 1, 0] [modp(n-1, 15)+1]): a:=n-> aa(n-6): seq(a(n), n=6..42); # Alois P. Heinz, Sep 08 2008
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MATHEMATICA
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etr[p_] := Module[{b}, b[n_] := b[n] = Module[{d, j}, If[n == 0, 1, Sum [Sum [d*p[d], {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]]; b]; aa = etr[ Function[n, {1, 1, 6, 1, 8, 6, 1, 1, 6, 8, 1, 6, 1, 1, 0}[[Mod[n-1, 15] + 1]]]]; a[n_] := aa[n-6]; Table[a[n], {n, 6, 41}] (* Jean-François Alcover, Mar 03 2014, after Alois P. Heinz *)
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PROG
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(PARI) {a(n) = local(A); if( n<6, 0, n -= 6; A = x * O(x^n); polcoeff( eta(x^15 + A)^13 / (eta(x + A) * eta(x^3 + A)^5 * eta(x^5 + A)^7), n))} /* Michael Somos, Nov 10 2005 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001
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STATUS
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approved
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