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%I #13 Jun 14 2024 08:49:00
%S 1,1,2,3,5,7,11,15,22,30,56,1002,10143,75175,451276,2323520,10619863,
%T 44108109,169229875,214481126,679903203,2056148051,5964539504,
%U 16670689208,45060624582,118159068427,301384802048,749474411781,1820701100652,4714566886083,10963707205259
%N Number of partitions of the n-th decimal palindrome.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Partition.html">Partition</a>
%F a(n) = A000041(A002113(n)).
%o (Python)
%o from sympy import npartitions
%o def A091582(n):
%o if n == 1: return 1
%o y = 10*(x:=10**(len(str(n>>1))-1))
%o return npartitions((c:=n-x)*x+int(str(c)[-2::-1]or 0) if n<x+y else (c:=n-y)*y+int(str(c)[-1::-1]or 0)) # _Chai Wah Wu_, Jun 14 2024
%Y Cf. A000041, A002113, A091584, A091583.
%K nonn,base
%O 1,3
%A _Reinhard Zumkeller_, Jan 22 2004
%E a(1)=1 prepended and more terms from _Georg Fischer_, Dec 15 2020