OFFSET
0,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..5000 (first 143 terms from Joerg Arndt)
Joerg Arndt, C++ program to compute this sequence, 2016
F. C. Auluck, On some new types of partitions associated with generalized Ferrers graphs, Proc. Cambridge Philos. Soc. 47 (1951), 679-686.
Anders Claesson, Svante Linusson, Henning Ulfarsson, and Emil Verkama, Inversion monotonicity in subclasses of the 1324-avoiders, arXiv:2604.01143 [math.CO], 2026. See pp. 25 (Prop. 5.13), 38 (Sect. 7.3).
Richard K. Guy, Letter to N. J. A. Sloane, Apr 08 1988 (annotated scanned copy, included with permission)
E. M. Wright, Stacks (III), Quart. J. Math. Oxford, 23 (1972), 153-158.
MAPLE
b:= proc(n, i, d) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, 1, b(n, i-1, d+1)+`if`(i>n, 0, d*b(n-i, i-1, 1))))
end:
a:= n-> b(n*(n-1)/2, n, 1):
seq(a(n), n=0..55); # Alois P. Heinz, Jul 08 2016
MATHEMATICA
b[n_, i_, d_] := b[n, i, d] = If[i*(i + 1)/2 < n, 0, If[n == 0, 1, b[n, i - 1, d + 1] + If[i > n, 0, d*b[n - i, i - 1, 1]]]];
a[n_] := b[n*(n - 1)/2, n, 1];
Table[a[n], {n, 0, 55}] (* Jean-François Alcover, Jul 28 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,nice,changed
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Jun 20 2015
Terms a(0)..a(11) computed by R. K. Guy
Terms a(12)=56 and beyond from Joerg Arndt, Apr 10 2016
STATUS
approved