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A320794 Number of multisets of exactly nine partitions of positive integers into distinct parts with total sum of parts equal to n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 16 20:13 EST 2019. Contains 329206 sequences. (Running on oeis4.)