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A319454 Number of partitions of 2n into exactly n nonzero decimal palindromes.

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