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A053762
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Number of 3-colored generalized Frobenius partitions of n.
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2
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1, 9, 27, 82, 207, 486, 1055, 2205, 4374, 8427, 15696, 28539, 50630, 88119, 150417, 252727, 418068, 682344, 1099343, 1750968, 2758185, 4301682, 6645150, 10175625, 15451744, 23281686, 34819227, 51712860, 76292784, 111850740, 162997314
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| G. E. Andrews, "Generalized Frobenius Partitions," AMS Memoir 301,1984 (sequence is denoted c\phi_3(n)).
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FORMULA
| Expansion of q^(1/8) * (eta(q)^3 + 9 * eta(q^9)^3) / (eta(q)^3 * eta(q^3)) in powers of q. - Michael Somos Mar 09 2011
Convolution of A000716 and A004016. - Michael Somos Mar 09 2011
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EXAMPLE
| 1 + 9*x + 27*x^2 + 82*x^3 + 207*x^4 + 486*x^5 + 1055*x^6 + 2205*x^7 + ...
1/q + 9*q^7 + 27*q^15 + 82*q^23 + 207*q^31 + 486*q^39 + 1055*q^47 + 2205*q^55 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^3 + 9 * x * eta(x^9 + A)^3) / (eta(x + A)^3 * eta(x^3 + A)), n))} /* Michael Somos Mar 09 2011 */
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CROSSREFS
| Cf. A000716, A004016, A051136.
Sequence in context: A053702 A036314 A036317 * A126322 A020279 A057901
Adjacent sequences: A053759 A053760 A053761 * A053763 A053764 A053765
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KEYWORD
| easy,nonn
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AUTHOR
| James A. Sellers (sellersj(AT)math.psu.edu), Apr 05 2000
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