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A319472 Number of partitions of n into exactly seven nonzero decimal palindromes.

%I A319472 #8 Sep 28 2018 05:51:22
%S A319472 0,0,0,0,0,0,0,1,1,2,3,5,7,11,15,21,27,37,46,60,73,91,108,131,151,178,
%T A319472 201,231,256,287,311,342,365,393,412,437,450,470,479,493,496,505,503,
%U A319472 508,503,504,496,496,487,487,479,478,472,473,469,472,471,476,477
%N A319472 Number of partitions of n into exactly seven nonzero decimal palindromes.
%H A319472 Alois P. Heinz, <a href="/A319472/b319472.txt">Table of n, a(n) for n = 0..10000</a>
%F A319472 a(n) = [x^n y^7] 1/Product_{j>=2} (1-y*x^A002113(j)).
%p A319472 p:= proc(n) option remember; local i, s; s:= ""||n;
%p A319472       for i to iquo(length(s), 2) do if
%p A319472         s[i]<>s[-i] then return false fi od; true
%p A319472     end:
%p A319472 h:= proc(n) option remember; `if`(n<1, 0,
%p A319472      `if`(p(n), n, h(n-1)))
%p A319472     end:
%p A319472 b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i<n,
%p A319472       0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p A319472     end:
%p A319472 a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(7):
%p A319472 seq(a(n), n=0..100);
%Y A319472 Column k=7 of A319453.
%Y A319472 Cf. A002113.
%K A319472 nonn,base,look
%O A319472 0,10
%A A319472 _Alois P. Heinz_, Sep 19 2018