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A061827 Number of partitions of n into parts which are the digits of n.

%I A061827 #36 Oct 27 2023 19:56:42
%S A061827 1,1,1,1,1,1,1,1,1,1,1,7,5,4,4,3,3,3,3,1,11,1,4,7,3,5,2,4,2,1,11,6,1,
%T A061827 3,3,7,2,2,5,1,11,11,4,1,3,4,2,7,2,1,11,6,4,3,1,2,2,2,2,1,11,11,11,6,
%U A061827 3,1,2,3,4,1,11,6,4,3,3,2,1,2,2,1,11,11,4,11,3,4,2,1,2,1,11,6,11,3,3,6,2,2
%N A061827 Number of partitions of n into parts which are the digits of n.
%C A061827 a(A125289(n)) = 1,  a(A125290(n)) > 1.
%H A061827 Alois P. Heinz, <a href="/A061827/b061827.txt">Table of n, a(n) for n = 1..15000</a> (first 1250 terms from Reinhard Zumkeller)
%e A061827 For n = 11, 1+1+1+1+1+1+1+1+1+1+1. so a(11) = 1. For n = 12, 2+2+2+2+2+2 = 2+2+1+1+1+1+1+1+1+1 = ...etc
%e A061827 a(20) = 1: the only partitions permitted use the digits 0 and 2, so there is just 1, 20 = 2+2+2... ten times.
%t A061827 Length[IntegerPartitions[#,All,DeleteDuplicates@DeleteCases[IntegerDigits[#],0]]]&/@Range[200] (* _Sander G. Huisman_, Nov 14 2022 *)
%o A061827 (Haskell)
%o A061827 import Data.List (sort, nub)
%o A061827 import Data.Char (digitToInt)
%o A061827 a061827 n =
%o A061827    p n (map digitToInt $ nub $ sort $ filter (/= '0') $ show n) where
%o A061827       p _ []        = 0
%o A061827       p 0 _         = 1
%o A061827       p m ds'@(d:ds)
%o A061827         | m < d     = 0
%o A061827         | otherwise = p (m - d) ds' + p m ds
%o A061827 -- _Reinhard Zumkeller_, Aug 01 2011
%Y A061827 Cf. A061828, A109950, A119999, A125291, A136460, A193513.
%K A061827 nonn,base,easy,look
%O A061827 1,12
%A A061827 _Amarnath Murthy_, May 28 2001
%E A061827 More terms from _David Wasserman_, Jul 29 2002