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A320791
Number of multisets of exactly six partitions of positive integers into distinct parts with total sum of parts equal to n.
2
1, 1, 3, 5, 11, 19, 37, 62, 112, 187, 320, 523, 866, 1386, 2229, 3510, 5516, 8538, 13172, 20073, 30461, 45781, 68469, 101586, 149991, 219922, 320925, 465492, 672055, 965063, 1379741, 1962957, 2781094, 3922672, 5511041, 7710818, 10748577, 14926037, 20654385
OFFSET
6,3
LINKS
FORMULA
a(n) = [x^n y^6] Product_{j>=1} 1/(1-y*x^j)^A000009(j).
MAPLE
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, 7)
end:
a:= n-> coeff(b(n$2), x, 6):
seq(a(n), n=6..60);
CROSSREFS
Column k=6 of A285229.
Cf. A000009.
Sequence in context: A320790 A175783 A078722 * A320792 A320793 A320794
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 21 2018
STATUS
approved