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Search: id:A104409
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| A104409 |
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Coefficients of the B-Rogers-Selberg identity. |
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+0
3
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| 1, 0, 0, 0, 1, -1, 1, -1, 2, -2, 2, -2, 4, -4, 4, -5, 7, -7, 8, -9, 12, -13, 14, -16, 21, -22, 24, -28, 34, -37, 41, -46, 55, -60, 66, -74, 87, -95, 104, -117, 135, -147, 162, -180, 205, -225, 246, -273, 309, -337, 369, -408, 457, -499, 546, -601, 669, -730, 796, -874, 969, -1055, 1149, -1259
(list; graph; listen)
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OFFSET
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0,9
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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^2, -q^5) / f(-q^2) in powers of q where f() is Ramanujan's theta function.
Euler transform of period 14 sequence [ 0, 0, 0, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, ...]. - Michael Somos Dec 04 2007
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EXAMPLE
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1 + q^4 - q^5 + q^6 - q^7 + 2*q^8 - 2*q^9 + 2*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, 0, 0, -1, 1, -1, 1, -1, 1, -1, 0, 0, 0][k%14+1]), n))} /* Michael Somos Dec 04 2007 */
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CROSSREFS
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Cf. A104408, A104410.
Sequence in context: A032544 A029079 A035398 this_sequence A032576 A071809 A104976
Adjacent sequences: A104406 A104407 A104408 this_sequence A104410 A104411 A104412
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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 06, 2005
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