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A319473 Number of partitions of n into exactly eight nonzero decimal palindromes.

%I A319473 #6 Sep 19 2018 17:09:42
%S A319473 0,0,0,0,0,0,0,0,1,1,2,3,5,7,11,15,22,28,39,49,65,80,102,123,152,179,
%T A319473 215,248,292,331,380,423,477,522,578,623,679,721,773,811,859,889,929,
%U A319473 953,985,1000,1025,1032,1050,1051,1063,1060,1068,1062,1068,1062,1068
%N A319473 Number of partitions of n into exactly eight nonzero decimal palindromes.
%H A319473 Alois P. Heinz, <a href="/A319473/b319473.txt">Table of n, a(n) for n = 0..10000</a>
%F A319473 a(n) = [x^n y^8] 1/Product_{j>=2} (1-y*x^A002113(j)).
%p A319473 p:= proc(n) option remember; local i, s; s:= ""||n;
%p A319473       for i to iquo(length(s), 2) do if
%p A319473         s[i]<>s[-i] then return false fi od; true
%p A319473     end:
%p A319473 h:= proc(n) option remember; `if`(n<1, 0,
%p A319473      `if`(p(n), n, h(n-1)))
%p A319473     end:
%p A319473 b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i<n,
%p A319473       0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p A319473     end:
%p A319473 a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(8):
%p A319473 seq(a(n), n=0..100);
%Y A319473 Column k=8 of A319453.
%Y A319473 Cf. A002113.
%K A319473 nonn,base
%O A319473 0,11
%A A319473 _Alois P. Heinz_, Sep 19 2018