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A327004
Irregular triangle read by rows in which the n-th row lists multinomials for partitions of 4n which have only parts which are multiples of 4, in Hindenburg order.
2
1, 1, 1, 35, 1, 495, 5775, 1, 1820, 6435, 450450, 2627625, 1, 4845, 125970, 4408950, 31177575, 727476750, 2546168625, 1, 10626, 735471, 25741485, 1352078, 1338557220, 15616500900, 1577585295, 165646455975, 1932541986375, 4509264634875
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, 35]
[3] [1, 495, 5775]
[4] [1, 1820, 6435, 450450, 2627625]
[5] [1, 4845, 125970, 4408950, 31177575, 727476750, 2546168625]
[6] [1, 10626, 735471, 25741485, 1352078, 1338557220, 15616500900, 1577585295, 165646455975, 1932541986375, 4509264634875]
PROG
(SageMath)
def A327004row(n):
shapes = ([4*x for x in p] for p in Partitions(n))
return [SetPartitions(sum(s), s).cardinality() for s in shapes]
for n in (0..6): print((A327004row(n)))
CROSSREFS
Cf. A000012 (m=0, subdivided into rows of length A000041), A080575 (m=1), A257490 (m=2), A327003 (m=3), this sequence (m=4).
Cf. A000041 (length of rows), A291975 (sum of rows), A291452 (coarser subdivision).
Cf. A260876.
Sequence in context: A365895 A176199 A059023 * A061045 A350805 A331040
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Aug 14 2019
STATUS
approved