A320794 Number of multisets of exactly nine partitions of positive integers into distinct parts with total sum of parts equal to n.

1, 1, 3, 5, 11, 19, 37, 63, 115, 195, 338, 563, 949, 1554, 2556, 4126, 6655, 10592, 16815, 26415, 41354, 64212, 99295, 152512, 233279, 354729, 537193, 809347, 1214485, 1814052, 2699197, 3999366, 5904074, 8682185, 12722807, 18576815, 27034032, 39208697

Offset

9,3

Links

Alois P. Heinz, Table of n, a(n) for n = 9..1000

Formula

a(n) = [x^n y^9] 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, 10)
    end:
a:= n-> coeff(b(n$2), x, 9):
seq(a(n), n=9..60);

Crossrefs

Column k=9 of A285229.

Cf. A000009.

Sequence in context: A320791 A320792 A320793 * A320795 A285230 A089098

Adjacent sequences: A320791 A320792 A320793 * A320795 A320796 A320797

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2018

Status

approved