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.

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]

Links

Table of n, a(n) for n=0..29.

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

Adjacent sequences: A327001 A327002 A327003 * A327005 A327006 A327007

Keyword

nonn,tabf

Author

Peter Luschny, Aug 14 2019

Status

approved