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A157407
The integer partitions of n taken as digits in base n+1 and listed in the reflected Hindenburg order.
1
0, 1, 4, 2, 21, 6, 3, 156, 32, 12, 8, 4, 1555, 260, 50, 45, 15, 10, 5, 19608, 2802, 408, 114, 402, 66, 24, 60, 18, 12, 6, 299593, 37450, 4690, 658, 4683, 595, 147, 91, 588, 84, 28, 77, 21, 14, 7
OFFSET
0,3
COMMENTS
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).
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.
EXAMPLE
[0] <-> [[ ]]
[1] <-> [[1]]
[4,2] <-> [[1,1],[2]]
[21,6,3] <-> [[1,1,1],[2,1],[3]]
[156,32,12,8,4] <-> [[1,1,1,1],[2,1,1],[2,2],[3,1],[4]]
MAPLE
a := proc(n) local rev, P, R, Q, i, l, s, k, j;
rev := l -> [seq(l[nops(l)-j+1], j=1..nops(l))];
P := combinat[partition](n); R := NULL;
for i to nops(P) do Q := rev(P[i]);
l := convert(Q, base, n+1, 10);
s := add(l[k]*10^(k-1), k=1..nops(l));
R:= R, s; od; R end: [0, seq(a(i), i=1..7)];
CROSSREFS
Sequence in context: A354094 A347590 A016517 * A100400 A285439 A336598
KEYWORD
easy,nonn,tabf,base
AUTHOR
Peter Luschny, Mar 11 2009
STATUS
approved