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Search: id:A051136
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| A051136 |
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Number of 2-colored generalized Frobenius partitions. |
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4
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| 1, 4, 9, 20, 42, 80, 147, 260, 445, 744, 1215, 1944, 3059, 4740, 7239, 10920, 16286, 24028, 35110, 50844, 73010, 104028, 147144, 206700, 288501, 400232, 552037, 757288, 1033495, 1403508, 1897088, 2552812, 3420527, 4564500, 6067265
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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G. E. Andrews, "Generalized Frobenius Partitions," AMS Memoir 301, 1984 (sequence is denoted c phi_2(n)).
G. E. Andrews, q-series, CBMS Regional Conference Series in Mathematics, 66, Amer. Math. Soc. 1986, see p. 67, Eq. (7.20). MR0858826 (88b:11063)
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FORMULA
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Expansion of phi(q) / f(-q)^2 in powers of q where phi(), f() are Ramanujan theta functions.
Expansion of q^(1/12) * eta(q^2)^5 / (eta(q)^4 * eta(q^4)^2) in powers of q. - Michael Somos, Apr 25 2003
Euler transform of period 4 sequence [ 4, -1, 4, 1, ...]. - Michael Somos, Apr 25 2003
G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = 24^(-1/2) (t/i)^(-1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A137828.
G.f.: Product_{k>0} (1 -x^(4*k-2)) / ((1 - x^(2*k-1))^4 * (1 - x^(4*k))).
G.f.: Product_{k>0} (1 + x^k)^3 / ((1 - x^k) * (1 + x^(2*k))^2). - Michael Somos Feb 12 2008 */
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EXAMPLE
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1/q + 4*q^11 + 9*q^23 + 20*q^35 + 42*q^47 + 80*q^59 + 147*q^71 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^5 / eta(x + A)^4 / eta(x^4 + A)^2, n))} /* Michael Somos Feb 12 2008 */
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CROSSREFS
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Sequence in context: A117074 A072934 A084639 this_sequence A156321 A133095 A132175
Adjacent sequences: A051133 A051134 A051135 this_sequence A051137 A051138 A051139
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KEYWORD
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easy,nonn
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AUTHOR
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James A. Sellers (sellersj(AT)math.psu.edu)
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