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A005575 a(n) = A259095(2n,n).
(Formerly M1390)
7

%I M1390

%S 0,0,1,2,5,11,20,37,63,110,174,283,435,671,1001,1492,2160,3127,4442,

%T 6269,8739,12109,16597,22618,30576,41077,54834,72788,96056,126131,

%U 164829,214327,277534,357810,459507,587779,749220,951473,1204501,1519691,1911618,2397247,2997985,3738482,4649981,5768457,7138640,8812704,10854735,13339286

%N a(n) = A259095(2n,n).

%C Computed by _R. K. Guy_ in 1988.

%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="/A005575/b005575.txt">Table of n, a(n) for n = 1..900</a>

%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://qjmath.oxfordjournals.org/content/23/2/153.extract">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, 1):

%p seq(a(n), n=1..50); # _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, 1];

%t Table[a[n], {n, 1, 50}] (* _Jean-Fran├žois Alcover_, Jul 28 2016, after _Alois P. Heinz_ *)

%Y Cf. A259095, A005576, A005577.

%K nonn,nice

%O 1,4

%A _N. J. A. Sloane_, _R. K. Guy_

%E Edited by _N. J. A. Sloane_, Jun 20 2015

%E Terms a(25) and beyond from _Joerg Arndt_, Apr 09 2016

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Last modified October 21 19:27 EDT 2018. Contains 316428 sequences. (Running on oeis4.)