A320791 - OEIS

%I #6 Oct 21 2018 09:37:47

%S 1,1,3,5,11,19,37,62,112,187,320,523,866,1386,2229,3510,5516,8538,

%T 13172,20073,30461,45781,68469,101586,149991,219922,320925,465492,

%U 672055,965063,1379741,1962957,2781094,3922672,5511041,7710818,10748577,14926037,20654385

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

%H Alois P. Heinz, <a href="/A320791/b320791.txt">Table of n, a(n) for n = 6..1000</a>

%F a(n) = [x^n y^6] 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, 7)

%p     end:

%p a:= n-> coeff(b(n$2), x, 6):

%p seq(a(n), n=6..60);

%Y Column k=6 of A285229.

%Y Cf. A000009.

%K nonn

%O 6,3

%A _Alois P. Heinz_, Oct 21 2018