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

8,3

Links

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

Formula

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

Crossrefs

Column k=8 of A285229.

Cf. A000009.

Sequence in context: A078722 A320791 A320792 * A320794 A320795 A285230

Adjacent sequences: A320790 A320791 A320792 * A320794 A320795 A320796

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2018

Status

approved