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A320792
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Number of multisets of exactly seven partitions of positive integers into distinct parts with total sum of parts equal to n.
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2
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1, 1, 3, 5, 11, 19, 37, 63, 114, 192, 331, 547, 914, 1482, 2412, 3847, 6126, 9620, 15052, 23292, 35889, 54806, 83294, 125658, 188656, 281418, 417828, 616838, 906516, 1325457, 1929644, 2796189, 4035315, 5798648, 8300214, 11833892, 16810048, 23790327, 33552202
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OFFSET
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7,3
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LINKS
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FORMULA
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a(n) = [x^n y^7] Product_{j>=1} 1/(1-y*x^j)^A000009(j).
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MAPLE
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g:= proc(n) option remember; `if`(n=0, 1, add(add(`if`(d::odd,
d, 0), d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
end:
b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*x^j*binomial(g(i)+j-1, j), j=0..n/i))), x, 8)
end:
a:= n-> coeff(b(n$2), x, 7):
seq(a(n), n=7..60);
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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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