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A319817 Number of partitions of n into exactly seven positive triangular numbers.

%I A319817 #4 Sep 28 2018 11:15:55
%S A319817 1,0,1,0,1,1,1,1,1,2,2,2,2,2,4,3,3,3,4,4,6,4,5,5,7,6,6,8,7,10,8,8,10,
%T A319817 10,11,11,12,11,14,14,13,14,16,15,17,18,17,20,19,20,21,22,21,22,27,23,
%U A319817 28,26,26,29,31,27,31,34,34,35,34,34,37,42,37,39,42
%N A319817 Number of partitions of n into exactly seven positive triangular numbers.
%H A319817 Alois P. Heinz, <a href="/A319817/b319817.txt">Table of n, a(n) for n = 7..10000</a>
%F A319817 a(n) = [x^n y^7] 1/Product_{j>=1} (1-y*x^A000217(j)).
%p A319817 h:= proc(n) option remember; `if`(n<1, 0,
%p A319817       `if`(issqr(8*n+1), n, h(n-1)))
%p A319817     end:
%p A319817 b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0), `if`(
%p A319817       k>n or i*k<n, 0, b(n, h(i-1), k)+b(n-i, h(min(n-i, i)), k-1)))
%p A319817     end:
%p A319817 a:= n-> b(n, h(n), 7):
%p A319817 seq(a(n), n=7..120);
%Y A319817 Column k=7 of A319797.
%Y A319817 Cf. A000217.
%K A319817 nonn
%O A319817 7,10
%A A319817 _Alois P. Heinz_, Sep 28 2018