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Search: id:A106407
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| A106407 |
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Expansion of x((1-x)(1-x^2)(1-x^4)(1-x^8)...)^2. |
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+0
1
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| 1, -2, -1, 4, -3, 2, 3, -8, 1, 6, -1, -4, 5, -6, -5, 16, -7, -2, 7, -12, 5, 2, -5, 8, 1, -10, -1, 12, -11, 10, 11, -32, 9, 14, -9, 4, 5, -14, -5, 24, -7, -10, 7, -4, -3, 10, 3, -16, 9, -2, -9, 20, -11, 2, 11, -24, 1, 22, -1, -20, 21, -22, -21, 64, -23, -18, 23, -28, 5, 18, -5, -8, 9, -10, -9, 28, -19, 10, 19, -48, 17, 14, -17, 20
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Euler transform of sequence b(n) where b(2^k)=-2 and zero otherwise.
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)=u1^3*u6 + 6*u1^2*u2*u6 + 9*u1*u2^2*u6 - u3*u2^3.
G.f. x(Product_{k>=0} (1-x^(2^k)))^2.
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=-v^3+4uvw+u^2w.
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PROGRAM
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(PARI) {a(n)=local(A, m); if(n<1, 0, n--; A=1+x*O(x^n); m=1; while(m<=n, A*=(1-x^m); m*=2; ); polcoeff(A^2, n))}
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CROSSREFS
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Sequence in context: A080079 A087712 A082467 this_sequence A023141 A072650 A082497
Adjacent sequences: A106404 A106405 A106406 this_sequence A106408 A106409 A106410
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KEYWORD
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sign
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AUTHOR
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Michael Somos, May 02 2005
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