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A320795 Number of multisets of exactly ten partitions of positive integers into distinct parts with total sum of parts equal to n.

%I A320795 #4 Oct 21 2018 09:45:28
%S A320795 1,1,3,5,11,19,37,63,115,195,339,565,954,1565,2580,4174,6751,10775,
%T A320795 17161,27051,42510,66261,102900,158746,243955,372778,567443,859492,
%U A320795 1296958,1948458,2916636,4348377,6460535,9563222,14109242,20744995,30405638,44422190
%N A320795 Number of multisets of exactly ten partitions of positive integers into distinct parts with total sum of parts equal to n.
%H A320795 Alois P. Heinz, <a href="/A320795/b320795.txt">Table of n, a(n) for n = 10..1000</a>
%F A320795 a(n) = [x^n y^10] Product_{j>=1} 1/(1-y*x^j)^A000009(j).
%p A320795 g:= proc(n) option remember; `if`(n=0, 1, add(add(`if`(d::odd,
%p A320795       d, 0), d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
%p A320795     end:
%p A320795 b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p A320795       add(b(n-i*j, i-1)*x^j*binomial(g(i)+j-1, j), j=0..n/i))), x, 11)
%p A320795     end:
%p A320795 a:= n-> coeff(b(n$2), x, 10):
%p A320795 seq(a(n), n=10..60);
%Y A320795 Column k=10 of A285229.
%Y A320795 Cf. A000009.
%K A320795 nonn
%O A320795 10,3
%A A320795 _Alois P. Heinz_, Oct 21 2018