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A157407 The integer partitions of n taken as digits in base n+1 and listed in the reflected Hindenburg order.

%I A157407 #5 Oct 04 2012 16:26:48
%S A157407 0,1,4,2,21,6,3,156,32,12,8,4,1555,260,50,45,15,10,5,19608,2802,408,
%T A157407 114,402,66,24,60,18,12,6,299593,37450,4690,658,4683,595,147,91,588,
%U A157407 84,28,77,21,14,7
%N A157407 The integer partitions of n taken as digits in base n+1 and listed in the reflected Hindenburg order.
%C A157407 The rows are enumerated 0,1,2,... Converting the numbers in the n-th row (n>0) to base n+1 gives all partitions of n in the 'reflected Hindenburg order'. The term 'reflected Hindenburg order' is not standard and refers to the partition generating algorithm of C. F. Hindenburg (1779).
%C A157407 The offset of row n (n>0) is A000070[n+1], the length of row n is A000041[n]. The left hand side of the triangle 0,1,4,21,156,... is A060072.
%H A157407 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%e A157407 [0] <-> [[ ]]
%e A157407 [1] <-> [[1]]
%e A157407 [4,2] <-> [[1,1],[2]]
%e A157407 [21,6,3] <-> [[1,1,1],[2,1],[3]]
%e A157407 [156,32,12,8,4] <-> [[1,1,1,1],[2,1,1],[2,2],[3,1],[4]]
%p A157407 a := proc(n) local rev,P,R,Q,i,l,s,k,j;
%p A157407 rev := l -> [seq(l[nops(l)-j+1],j=1..nops(l))];
%p A157407 P := combinat[partition](n); R := NULL;
%p A157407 for i to nops(P) do Q := rev(P[i]);
%p A157407 l := convert(Q,base,n+1,10);
%p A157407 s := add(l[k]*10^(k-1), k=1..nops(l));
%p A157407 R:= R,s; od; R end: [0,seq(a(i),i=1..7)];
%Y A157407 Cf. A157406
%K A157407 easy,nonn,tabf,base
%O A157407 0,3
%A A157407 _Peter Luschny_, Mar 11 2009