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A157406 The integer partitions of n taken as digits in base n+1 and listed in the Hindenburg order.

%I A157406 #5 Oct 04 2012 16:26:36
%S A157406 0,1,2,4,3,9,21,4,16,12,56,156,5,25,20,115,85,475,1555,6,36,30,204,24,
%T A157406 162,1086,114,792,5202,19608,7,49,42,329,35,273,2121,217,210,1673,
%U A157406 12873,1169,9289,70217,299593
%N A157406 The integer partitions of n taken as digits in base n+1 and listed in the Hindenburg order.
%C A157406 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 'Hindenburg order'. The term 'Hindenburg order' is not standard and refers to the partition generating algorithm of C. F. Hindenburg (1779).
%C A157406 The offset of row n (n>0) is A000070[n+1], the length of row n is A000041[n]. The right hand side of the triangle 0,1,4,21,156,... is A060072.
%H A157406 Peter Luschny, <a href="http://www.luschny.de/math/seq/CountingWithPartitions.html"> Counting with Partitions</a>.
%e A157406 [0] <-> [[ ]]
%e A157406 [1] <-> [[1]]
%e A157406 [2,4] <-> [[2],[1,1]]
%e A157406 [3,9,21] <-> [[3],[1,2],[1,1,1]]
%e A157406 [4,16,12,56,156] <-> [[4],[1,3],[2,2],[1,1,2],[1,1,1,1]]
%p A157406 a := proc(n) local rev,P,R,i,l,s,k,j;
%p A157406 rev := l -> [seq(l[nops(l)-j+1],j=1..nops(l))];
%p A157406 P := rev(combinat[partition](n)); R := NULL;
%p A157406 for i to nops(P) do l := convert(P[i],base,n+1,10);
%p A157406 s := add(l[k]*10^(k-1),k=1..nops(l));
%p A157406 R := R,s; od; R end: [0,seq(a(i),i=1..7)];
%Y A157406 Cf. A157407
%K A157406 easy,nonn,tabf,base
%O A157406 0,3
%A A157406 _Peter Luschny_, Mar 11 2009