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%I #6 Sep 19 2018 17:10:05
%S 0,0,0,0,0,0,0,0,0,1,1,2,3,5,7,11,15,22,29,40,51,68,85,109,134,167,
%T 200,244,286,341,395,460,523,600,671,756,835,926,1008,1103,1185,1280,
%U 1360,1450,1524,1609,1673,1748,1803,1867,1910,1965,1996,2039,2063,2096
%N Number of partitions of n into exactly nine nonzero decimal palindromes.
%H Alois P. Heinz, <a href="/A319474/b319474.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = [x^n y^9] 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))(9):
%p seq(a(n), n=0..100);
%Y Column k=9 of A319453.
%Y Cf. A002113.
%K nonn,base
%O 0,12
%A _Alois P. Heinz_, Sep 19 2018
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