OFFSET
0,4
COMMENTS
The Hindenburg order refers to the partition generating algorithm of C. F. Hindenburg (1779). [Knuth 7.2.1.4H]
FORMULA
Row of lengths are in A000041.
EXAMPLE
The irregular triangle starts:
[0] [1]
[1] [1]
[2] [1, 10]
[3] [1, 84, 280]
[4] [1, 220, 462, 9240, 15400]
[5] [1, 455, 5005, 50050, 210210, 1401400, 1401400]
[6] [1, 816, 18564, 185640, 24310, 4084080, 13613600, 2858856, 85765680, 285885600, 190590400]
PROG
(SageMath)
def A327003row(n):
shapes = ([3*x for x in p] for p in Partitions(n))
return [SetPartitions(sum(s), s).cardinality() for s in shapes]
for n in (0..7): print(A327003row(n))
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Aug 14 2019
STATUS
approved