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A348163
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Number of partitions of n such that 4*(greatest part) = (number of parts).
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2
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0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 2, 3, 4, 5, 6, 8, 9, 12, 14, 16, 18, 22, 25, 30, 35, 42, 49, 60, 68, 81, 93, 109, 127, 149, 171, 200, 231, 269, 309, 359, 410, 474, 544, 625, 715, 824, 939, 1080, 1232, 1411, 1607, 1839, 2090, 2385, 2708, 3081, 3493, 3972, 4493
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OFFSET
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1,14
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COMMENTS
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Also, the number of partitions of n such that (greatest part) = 4*(number of parts).
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} x^(5*k-1) * Product_{j=1..k-1} (1-x^(4*k+j-1)/(1-x^j).
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EXAMPLE
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a(16) = 3 counts these partitions:
[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[2, 2, 2, 2, 2, 2, 2, 2].
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PROG
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(PARI) my(N=66, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=1, N, x^(5*k-1)*prod(j=1, k-1, (1-x^(4*k+j-1))/(1-x^j)))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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