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A103261
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Number of partitions of 2n into parts with 10 types c^1 c^2...C^10 of each part. The even parts appear with multiplicity 1 for each type . The odd parts occur with multiplicity 2 for each part.
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0
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1, 20, 200, 1360, 7200, 32024, 125280, 443680, 1450240, 4435940, 12827888, 35346800, 93377920, 237675640, 585229760, 1398704736, 3253934080, 7386124520, 16392493800, 35634450320, 75992326592, 159199081600, 328027789600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This is also Sequence(A080054)^(10) or sequence(A007096)^(5)
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FORMULA
| G.f.:(theta_4(0, x^2)/theta_4(0, x))^10= (theta_3(0, x)/theta_4(0, x))^5.
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EXAMPLE
| a(4)=200 because we have 10 types of 4, 45 ways of writing 4 in terms of ten of 2's only or ten of 11's only and 100 ways of writing 2's combined with 11's so the total number of ways of writng 4 is 200.
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MAPLE
| series(product(((1+x^k)*(1-x^(2*k)))^(10)/((1-x^k)*(1+x^(2*k)))^(10), k=1..100), x=0, 100);
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CROSSREFS
| Cf. A080054, A007096.
Sequence in context: A008420 A045758 A035474 * A120796 A120787 A099197
Adjacent sequences: A103258 A103259 A103260 * A103262 A103263 A103264
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KEYWORD
| nonn
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AUTHOR
| Noureddine Chair (n.chair(AT)rocketmail.com), Feb 16 2005
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