cp's OEIS Frontend

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

%I A320794 #4 Oct 21 2018 09:43:03
%S A320794 1,1,3,5,11,19,37,63,115,195,338,563,949,1554,2556,4126,6655,10592,
%T A320794 16815,26415,41354,64212,99295,152512,233279,354729,537193,809347,
%U A320794 1214485,1814052,2699197,3999366,5904074,8682185,12722807,18576815,27034032,39208697
%N A320794 Number of multisets of exactly nine partitions of positive integers into distinct parts with total sum of parts equal to n.
%H A320794 Alois P. Heinz, <a href="/A320794/b320794.txt">Table of n, a(n) for n = 9..1000</a>
%F A320794 a(n) = [x^n y^9] Product_{j>=1} 1/(1-y*x^j)^A000009(j).
%p A320794 g:= proc(n) option remember; `if`(n=0, 1, add(add(`if`(d::odd,
%p A320794       d, 0), d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
%p A320794     end:
%p A320794 b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p A320794       add(b(n-i*j, i-1)*x^j*binomial(g(i)+j-1, j), j=0..n/i))), x, 10)
%p A320794     end:
%p A320794 a:= n-> coeff(b(n$2), x, 9):
%p A320794 seq(a(n), n=9..60);
%Y A320794 Column k=9 of A285229.
%Y A320794 Cf. A000009.
%K A320794 nonn
%O A320794 9,3
%A A320794 _Alois P. Heinz_, Oct 21 2018