cp's OEIS Frontend

A320792 Number of multisets of exactly seven partitions of positive integers into distinct parts with total sum of parts equal to n.

%I A320792 #4 Oct 21 2018 09:35:21
%S A320792 1,1,3,5,11,19,37,63,114,192,331,547,914,1482,2412,3847,6126,9620,
%T A320792 15052,23292,35889,54806,83294,125658,188656,281418,417828,616838,
%U A320792 906516,1325457,1929644,2796189,4035315,5798648,8300214,11833892,16810048,23790327,33552202
%N A320792 Number of multisets of exactly seven partitions of positive integers into distinct parts with total sum of parts equal to n.
%H A320792 Alois P. Heinz, <a href="/A320792/b320792.txt">Table of n, a(n) for n = 7..1000</a>
%F A320792 a(n) = [x^n y^7] Product_{j>=1} 1/(1-y*x^j)^A000009(j).
%p A320792 g:= proc(n) option remember; `if`(n=0, 1, add(add(`if`(d::odd,
%p A320792       d, 0), d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
%p A320792     end:
%p A320792 b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
%p A320792       add(b(n-i*j, i-1)*x^j*binomial(g(i)+j-1, j), j=0..n/i))), x, 8)
%p A320792     end:
%p A320792 a:= n-> coeff(b(n$2), x, 7):
%p A320792 seq(a(n), n=7..60);
%Y A320792 Column k=7 of A285229.
%Y A320792 Cf. A000009.
%K A320792 nonn
%O A320792 7,3
%A A320792 _Alois P. Heinz_, Oct 21 2018