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%I #8 Sep 28 2018 05:51:22
%S 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 201,231,256,287,311,342,365,393,412,437,450,470,479,493,496,505,503,
%U 508,503,504,496,496,487,487,479,478,472,473,469,472,471,476,477
%N Number of partitions of n into exactly seven nonzero decimal palindromes.
%H Alois P. Heinz, <a href="/A319472/b319472.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = [x^n y^7] 1/Product_{j>=2} (1-y*x^A002113(j)).
%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`(t*i<n,
%p 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p end:
%p a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(7):
%p seq(a(n), n=0..100);
%Y Column k=7 of A319453.
%Y Cf. A002113.
%K nonn,base,look
%O 0,10
%A _Alois P. Heinz_, Sep 19 2018
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