A320791 Number of multisets of exactly six partitions of positive integers into distinct parts with total sum of parts equal to n.

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

Alois P. Heinz, Table of n, a(n) for n = 6..1000

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

Adjacent sequences: A320788 A320789 A320790 * A320792 A320793 A320794

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2018

Status

approved