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%I M0583 #45 Oct 29 2023 21:12:01
%S 1,1,2,3,4,7,9,13,17,25,32,43,56,73,95,122,155,196,248,309,388,480,
%T 595,731,899,1096,1338,1624,1967,2373,2860,3431,4111,4911,5853,6963,
%U 8263,9785,11565,13646,16064,18884,22155,25953,30349,35441,41311,48098,55906,64900,75231,87103,100702,116296,134130,154522
%N The limiting sequence [A259095(r(r+1)/2-s,r), s=0,1,2,...,r-1] for very large r.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A005576/b005576.txt">Table of n, a(n) for n = 0..5000</a> (first 143 terms from Joerg Arndt)
%H Joerg Arndt, <a href="http://jjj.de/fxt/demo/seq/#A005576">C++ program to compute this sequence</a>, 2016
%H F. C. Auluck, <a href="http://dx.doi.org/10.1017/S0305004100027134">On some new types of partitions associated with generalized Ferrers graphs</a>, Proc. Cambridge Philos. Soc. 47, (1951), 679-686.
%H R. K. Guy, <a href="/A259095/a259095.pdf">Letter to N. J. A. Sloane, Apr 08 1988</a> (annotated scanned copy, included with permission)
%H E. M. Wright, <a href="http://dx.doi.org/10.1093/qmath/23.2.153">Stacks (III)</a>, Quart. J. Math. Oxford, 23 (1972), 153-158.
%p b:= proc(n, i, d) option remember; `if`(i*(i+1)/2<n, 0,
%p `if`(n=0, 1, b(n, i-1, d+1)+`if`(i>n, 0, d*b(n-i, i-1, 1))))
%p end:
%p a:= n-> b(n*(n-1)/2, n, 1):
%p seq(a(n), n=0..55); # _Alois P. Heinz_, Jul 08 2016
%t 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]]]];
%t a[n_] := b[n*(n - 1)/2, n, 1];
%t Table[a[n], {n, 0, 55}] (* _Jean-François Alcover_, Jul 28 2016, after _Alois P. Heinz_ *)
%Y Cf. A259095, A005575, A005577.
%K nonn,nice
%O 0,3
%A _N. J. A. Sloane_, _R. K. Guy_
%E Edited by _N. J. A. Sloane_, Jun 20 2015
%E Terms a(0)..a(11) computed by _R. K. Guy_
%E Terms a(12)=56 and beyond from _Joerg Arndt_, Apr 10 2016
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