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Search: id:A104408
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| A104408 |
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Coefficients of the A-Rogers-Selberg identity. |
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+0
3
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| 1, 0, 1, -1, 1, -1, 2, -2, 3, -3, 4, -5, 6, -6, 8, -9, 11, -12, 15, -17, 20, -22, 26, -30, 35, -38, 45, -51, 58, -64, 74, -83, 95, -105, 119, -134, 151, -166, 188, -210, 235, -259, 291, -323, 360, -396, 441, -489, 543, -595, 661, -730, 805, -883, 976, -1073, 1182, -1293, 1423, -1562, 1714
(list; graph; listen)
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OFFSET
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0,7
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LINKS
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Eric Weisstein's World of Mathematics, Rogers-Selberg Identities
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FORMULA
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Expansion of f(-q^3, -q^4) / f(-q^2) in powers of q where f() is Ramanujan's theta function.
Euler transform of period 14 sequence [ 0, 1, -1, 0, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, ...]. - Michael Somos Dec 04 2007
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EXAMPLE
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1 + q^2 - q^3 + q^4 - q^5 + 2*q^6 - 2*q^7 + 3*q^8 - 3*q^9 + 4*q^10 + ...
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PROGRAM
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(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x*O(x^n))^[0, 0, -1, 1, 0, 0, -1, 1, -1, 0, 0, 1, -1, 0][k%14+1]), n))} /* Michael Somos Dec 04 2007 */
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CROSSREFS
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Cf. A104409, A104410.
Sequence in context: A143738 A029071 A117144 this_sequence A008718 A030719 A126027
Adjacent sequences: A104405 A104406 A104407 this_sequence A104409 A104410 A104411
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KEYWORD
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sign
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Mar 05, 2005
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