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A320795
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Number of multisets of exactly ten 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, 115, 195, 339, 565, 954, 1565, 2580, 4174, 6751, 10775, 17161, 27051, 42510, 66261, 102900, 158746, 243955, 372778, 567443, 859492, 1296958, 1948458, 2916636, 4348377, 6460535, 9563222, 14109242, 20744995, 30405638, 44422190
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OFFSET
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10,3
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LINKS
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FORMULA
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a(n) = [x^n y^10] 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, 11)
end:
a:= n-> coeff(b(n$2), x, 10):
seq(a(n), n=10..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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