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A327003
Irregular triangle read by rows in which the n-th row lists multinomials for partitions of 3n which have only parts which are multiples of 3, in Hindenburg order.
2
1, 1, 1, 10, 1, 84, 280, 1, 220, 462, 9240, 15400, 1, 455, 5005, 50050, 210210, 1401400, 1401400, 1, 816, 18564, 185640, 24310, 4084080, 13613600, 2858856, 85765680, 285885600, 190590400, 1, 1330, 54264, 542640, 293930, 24690120, 82300400, 32332300, 135795660, 2715913200, 4526522000, 3802278480, 38022784800, 76045569600, 36212176000
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
Cf. A000012 (m=0, subdivided into rows of length A000041), A080575 (m=1), A257490 (m=2), this sequence (m=3), A327004 (m=4).
Cf. A000041 (length of rows), A291973 (sum of rows), A291451 (coarser subdivision).
Cf. A260876.
Sequence in context: A009227 A305996 A030526 * A206819 A178865 A347491
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Aug 14 2019
STATUS
approved