A320793 - OEIS

%I #4 Oct 21 2018 09:40:29

%S 1,1,3,5,11,19,37,63,115,194,336,558,938,1530,2508,4030,6472,10246,

%T 16179,25270,39325,60664,93187,142119,215800,325647,489288,731154,

%U 1087981,1611036,2375905,3488306,5101755,7430869,10783473,15589092,22457429,32236645

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

%H Alois P. Heinz, <a href="/A320793/b320793.txt">Table of n, a(n) for n = 8..1000</a>

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

%p g:= proc(n) option remember; `if`(n=0, 1, add(add(`if`(d::odd,

%p       d, 0), d=numtheory[divisors](j))*g(n-j), j=1..n)/n)

%p     end:

%p b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,

%p       add(b(n-i*j, i-1)*x^j*binomial(g(i)+j-1, j), j=0..n/i))), x, 9)

%p     end:

%p a:= n-> coeff(b(n$2), x, 8):

%p seq(a(n), n=8..60);

%Y Column k=8 of A285229.

%Y Cf. A000009.

%K nonn

%O 8,3

%A _Alois P. Heinz_, Oct 21 2018