A320793 Number of multisets of exactly eight partitions of positive integers into distinct parts with total sum of parts equal to n.

1, 1, 3, 5, 11, 19, 37, 63, 115, 194, 336, 558, 938, 1530, 2508, 4030, 6472, 10246, 16179, 25270, 39325, 60664, 93187, 142119, 215800, 325647, 489288, 731154, 1087981, 1611036, 2375905, 3488306, 5101755, 7430869, 10783473, 15589092, 22457429, 32236645

Offset: 8

Author

Alois P. Heinz, Oct 21 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..1000

Crossrefs

Column k=8 of A285229.

Cf. A000009.

Programs

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, 9)
    end:
a:= n-> coeff(b(n$2), x, 8):
seq(a(n), n=8..60);

Formula

a(n) = [x^n y^8] Product_{j>=1} 1/(1-y*x^j)^A000009(j).