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%I #9 Sep 19 2018 17:08:16
%S 0,0,0,0,0,1,1,2,3,5,7,10,13,18,22,29,34,42,48,57,63,72,77,85,88,95,
%T 96,100,99,101,98,98,93,92,87,85,80,79,74,73,70,69,67,67,65,66,65,66,
%U 66,67,68,69,70,72,73,75,76,78,79,81,81,83,83,84,84,85,84
%N Number of partitions of n into exactly five nonzero decimal palindromes.
%H Alois P. Heinz, <a href="/A319470/b319470.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = [x^n y^5] 1/Product_{j>=2} (1-y*x^A002113(j)).
%p p:= proc(n) option remember; local i, s; s:= ""||n;
%p for i to iquo(length(s), 2) do if
%p s[i]<>s[-i] then return false fi od; true
%p end:
%p h:= proc(n) option remember; `if`(n<1, 0,
%p `if`(p(n), n, h(n-1)))
%p end:
%p b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i<n,
%p 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p end:
%p a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(5):
%p seq(a(n), n=0..100);
%Y Column k=5 of A319453.
%Y Cf. A002113.
%K nonn,base
%O 0,8
%A _Alois P. Heinz_, Sep 19 2018
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