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A122777
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Coefficients of L-series for elliptic curve "30a1": y^2 + x * y + y = x^3 + x + 2.
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1
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1, -1, 1, 1, -1, -1, -4, -1, 1, 1, 0, 1, 2, 4, -1, 1, 6, -1, -4, -1, -4, 0, 0, -1, 1, -2, 1, -4, -6, 1, 8, -1, 0, -6, 4, 1, 2, 4, 2, 1, -6, 4, -4, 0, -1, 0, 0, 1, 9, -1, 6, 2, -6, -1, 0, 4, -4, 6, 0, -1, -10, -8, -4, 1, -2, 0, -4, 6, 0, -4, 0, -1, 2, -2, 1, -4, 0, -2, 8, -1, 1, 6, 12, -4, -6, 4, -6, 0, 18, 1, -8, 0, 8, 0, 4, -1, 2, -9, 0, 1, 18, -6, -4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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FORMULA
| Expansion of eta(q^3) * eta(q^5) * eta(q^6) * eta(q^10) - eta(q) * eta(q^2) * eta(q^15) * eta(q^30) in powers of q.
G.f.: x Product_{k>0} (1-x^(3k))(1-x^(5k))(1-x^(6k))(1-x^(10k)) - x^2 Product_{k>0} (1-x^k)(1-x^(2k))(1-x^(15k))(1-x^(30k)).
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PROG
| (PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^3 + A) * eta(x^5 + A) * eta(x^6 + A) * eta(x^10 + A) - eta(x + A) * eta(x^2 + A) * eta(x^15 + A) * eta(x^30 + A) * x, n))}
(PARI) {a(n) = local(A); if( n<1, 0, n*=2; n--; A = x * O(x^n); A = eta(x^2 + A) * eta(x^3 + A)^3 / (eta(x + A) * eta(x^6 + A)); A = A * subst(A + x * O(x^(n\5)), x, x^5); polcoeff(A, n))}
(PARI) {a(n) = local(A, p, e, x, y, a0, a1); if( n<1, 0, A = factor(n); prod( k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if( p==2 | p==5, (-1)^e, if( p==3, 1, a1 = y =- sum(x=0, p-1, kronecker( 6*x^3 + x^2 + 4*x + 4, p)); a0 = 1; for(i=2, e, x = y * a1 - p * a0; a0 = a1; a1 = x); a1)))))}
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CROSSREFS
| A122779(2n)=a(n).
Sequence in context: A128760 A057884 A016684 * A103524 A110916 A185058
Adjacent sequences: A122774 A122775 A122776 * A122778 A122779 A122780
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KEYWORD
| sign,mult
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AUTHOR
| Michael Somos, Sep 10 2006
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