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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.

%I A327004 #10 Feb 29 2020 04:22:55
%S A327004 1,1,1,35,1,495,5775,1,1820,6435,450450,2627625,1,4845,125970,4408950,
%T A327004 31177575,727476750,2546168625,1,10626,735471,25741485,1352078,
%U A327004 1338557220,15616500900,1577585295,165646455975,1932541986375,4509264634875
%N 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.
%C A327004 The Hindenburg order refers to the partition generating algorithm of C. F. Hindenburg (1779). [Knuth 7.2.1.4H]
%F A327004 Row of lengths are in A000041.
%e A327004 The irregular triangle starts:
%e A327004 [0] [1]
%e A327004 [1] [1]
%e A327004 [2] [1, 35]
%e A327004 [3] [1, 495, 5775]
%e A327004 [4] [1, 1820, 6435, 450450, 2627625]
%e A327004 [5] [1, 4845, 125970, 4408950, 31177575, 727476750, 2546168625]
%e A327004 [6] [1, 10626, 735471, 25741485, 1352078, 1338557220, 15616500900, 1577585295, 165646455975, 1932541986375, 4509264634875]
%o A327004 (SageMath)
%o A327004 def A327004row(n):
%o A327004     shapes = ([4*x for x in p] for p in Partitions(n))
%o A327004     return [SetPartitions(sum(s), s).cardinality() for s in shapes]
%o A327004 for n in (0..6): print((A327004row(n)))
%Y A327004 Cf. A000012 (m=0, subdivided into rows of length A000041), A080575 (m=1), A257490 (m=2), A327003 (m=3), this sequence (m=4).
%Y A327004 Cf. A000041 (length of rows), A291975 (sum of rows), A291452 (coarser subdivision).
%Y A327004 Cf. A260876.
%K A327004 nonn,tabf
%O A327004 0,4
%A A327004 _Peter Luschny_, Aug 14 2019