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A319820 Number of partitions of n into exactly ten positive triangular numbers.

%I A319820 #4 Sep 28 2018 11:26:48
%S A319820 1,0,1,0,1,1,1,1,1,2,2,2,2,2,4,3,4,3,5,5,7,5,6,7,8,8,8,10,10,12,12,11,
%T A319820 14,14,16,16,17,18,20,21,21,23,25,24,29,29,29,32,33,35,36,39,38,41,47,
%U A319820 44,50,48,52,55,58,55,62,66,66,70,71,72,78,84,82,84
%N A319820 Number of partitions of n into exactly ten positive triangular numbers.
%H A319820 Alois P. Heinz, <a href="/A319820/b319820.txt">Table of n, a(n) for n = 10..10000</a>
%F A319820 a(n) = [x^n y^10] 1/Product_{j>=1} (1-y*x^A000217(j)).
%p A319820 h:= proc(n) option remember; `if`(n<1, 0,
%p A319820       `if`(issqr(8*n+1), n, h(n-1)))
%p A319820     end:
%p A319820 b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0), `if`(
%p A319820       k>n or i*k<n, 0, b(n, h(i-1), k)+b(n-i, h(min(n-i, i)), k-1)))
%p A319820     end:
%p A319820 a:= n-> b(n, h(n), 10):
%p A319820 seq(a(n), n=10..120);
%Y A319820 Column k=10 of A319797.
%Y A319820 Cf. A000217.
%K A319820 nonn
%O A319820 10,10
%A A319820 _Alois P. Heinz_, Sep 28 2018