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A319475 Number of partitions of n into exactly ten nonzero decimal palindromes.

%I A319475 #6 Sep 19 2018 17:10:23
%S A319475 0,0,0,0,0,0,0,0,0,0,1,1,2,3,5,7,11,15,22,29,41,52,70,88,114,141,178,
%T A319475 215,265,315,380,445,526,606,705,801,916,1027,1159,1282,1427,1561,
%U A319475 1715,1855,2015,2157,2318,2458,2614,2747,2897,3018,3157,3266,3390,3485
%N A319475 Number of partitions of n into exactly ten nonzero decimal palindromes.
%H A319475 Alois P. Heinz, <a href="/A319475/b319475.txt">Table of n, a(n) for n = 0..10000</a>
%F A319475 a(n) = [x^n y^10] 1/Product_{j>=2} (1-y*x^A002113(j)).
%p A319475 p:= proc(n) option remember; local i, s; s:= ""||n;
%p A319475       for i to iquo(length(s), 2) do if
%p A319475         s[i]<>s[-i] then return false fi od; true
%p A319475     end:
%p A319475 h:= proc(n) option remember; `if`(n<1, 0,
%p A319475      `if`(p(n), n, h(n-1)))
%p A319475     end:
%p A319475 b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i<n,
%p A319475       0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p A319475     end:
%p A319475 a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(10):
%p A319475 seq(a(n), n=0..100);
%Y A319475 Column k=10 of A319453.
%Y A319475 Cf. A002113.
%K A319475 nonn,base
%O A319475 0,13
%A A319475 _Alois P. Heinz_, Sep 19 2018