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A104410
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Coefficients of the C-Rogers-Selberg identity.
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2
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1, -1, 1, -1, 2, -2, 2, -3, 4, -4, 5, -6, 8, -9, 10, -12, 15, -17, 19, -22, 27, -30, 34, -39, 46, -52, 58, -66, 77, -86, 96, -109, 125, -139, 155, -174, 198, -220, 244, -273, 308, -341, 377, -420, 470, -519, 573, -635, 707, -779, 857, -946, 1049, -1152, 1264, -1392, 1536, -1683, 1843, -2022, 2224
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OFFSET
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0,5
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LINKS
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Table of n, a(n) for n=0..60.
Eric Weisstein's World of Mathematics, Rogers-Selberg Identities
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FORMULA
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Expansion of f(-q, -q^6) / f(-q^2) in powers of q where f() is Ramanujan's theta function.
Euler transform of period 14 sequence [ -1, 1, 0, 1, 0, 0, -1, 0, 0, 1, 0, 1, -1, 0, ...]. - Michael Somos Dec 04 2007
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EXAMPLE
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1 - q + q^2 - q^3 + 2*q^4 - 2*q^5 + 2*q^6 - 3*q^7 + 4*q^8 - 4*q^9 + 5*q^10 + ...
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PROG
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(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x*O(x^n))^[0, 1, -1, 0, -1, 0, 0, 1, 0, 0, -1, 0, -1, 1][k%14+1]), n))} /* Michael Somos Dec 04 2007 */
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CROSSREFS
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Cf. A104408, A104409.
Sequence in context: A173911 A076269 A143644 * A018048 A077564 A088044
Adjacent sequences: A104407 A104408 A104409 * A104411 A104412 A104413
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KEYWORD
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sign
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AUTHOR
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Eric W. Weisstein, Mar 06, 2005
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STATUS
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approved
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