%I #8 Sep 19 2018 16:12:06
%S 1,1,2,3,5,7,11,15,22,29,41,53,72,92,121,153,197,245,310,381,475,579,
%T 711,858,1043,1248,1501,1783,2126,2507,2966,3476,4083,4757,5551,6433,
%U 7464,8606,9931,11398,13089,14957,17099,19461,22153,25120,28483,32183,36361
%N Number of partitions of 2n into exactly n nonzero decimal palindromes.
%H Alois P. Heinz, <a href="/A319454/b319454.txt">Table of n, a(n) for n = 0..1500</a>
%F a(n) = [x^(2n) y^n] 1/Product_{j>=2} (1-y*x^A002113(j)).
%F a(n) = A319453(2n,n).
%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`(i<1 or
%p t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p end:
%p a:= n-> `if`(n=0, 1, b(2*n, h(2*n), n)-b(2*n, h(2*n), n-1)):
%p seq(a(n), n=0..70);
%Y Cf. A002113, A319453.
%K nonn,base
%O 0,3
%A _Alois P. Heinz_, Sep 19 2018