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A104409
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Coefficients of the B-Rogers-Selberg identity.
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2
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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; refs; listen; history; internal format)
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OFFSET
| 0,9
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LINKS
| Eric Weisstein's World of Mathematics, Rogers-Selberg Identities
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FORMULA
| 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
| 1 + q^4 - q^5 + q^6 - q^7 + 2*q^8 - 2*q^9 + 2*q^10 + ...
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PROG
| (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
| Cf. A104408, A104410.
Sequence in context: A200675 A029079 A035398 * A032576 A071809 A104976
Adjacent sequences: A104406 A104407 A104408 * A104410 A104411 A104412
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KEYWORD
| sign
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Mar 06, 2005
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