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%I #12 Jun 21 2018 02:23:40
%S 1,1,1,1,1,2,1,3,1,4,1,1,5,3,1,6,6,1,7,10,1,8,15,1,1,9,21,4,1,10,28,
%T 10,1,11,36,20,1,12,45,35,1,13,55,56,1,1,14,66,84,5,1,15,78,120,15,1,
%U 16,91,165,35,1,17,105,220,70,1,18,120,286,126,1,19,136,364,210,1,1,20,153,455
%N Irregular triangle read by rows: T(n,k) is the number of superdiagonal bargraphs with area n and with k columns.
%H Emeric Deutsch, Emanuele Munarini, Simone Rinaldi, <a href="http://dx.doi.org/10.1016/j.jspi.2009.12.013">Skew Dyck paths, area, and superdiagonal bargraphs</a>, Journal of Statistical Planning and Inference, Vol. 140, Issue 6, June 2010, pp. 1550-1562.
%F T(n,k) = binomial(n-1-k*(k-1)/2,k-1), 1<=k <= (sqrt(1+8*n)-1)/2.
%e 1,
%e 1,
%e 1, 1,
%e 1, 2,
%e 1, 3,
%e 1, 4, 1,
%e 1, 5, 3,
%e 1, 6, 6,
%e 1, 7, 10,
%e 1, 8, 15, 1,
%e 1, 9, 21, 4,
%e 1, 10, 28, 10,
%e 1, 11, 36, 20,
%e 1, 12, 45, 35,
%e 1, 13, 55, 56, 1,
%e 1, 14, 66, 84, 5,
%e 1, 15, 78, 120, 15,
%e 1, 16, 91, 165, 35,
%e 1, 17, 105, 220, 70,
%e 1, 18, 120, 286, 126,
%e 1, 19, 136, 364, 210, 1,
%e 1, 20, 153, 455, 330, 6,
%e 1, 21, 171, 560, 495, 21,
%e 1, 22, 190, 680, 715, 56,
%e 1, 23, 210, 816,1001, 126,
%e 1, 24, 231, 969,1365, 252,
%e 1, 25, 253,1140,1820, 462,
%e 1, 26, 276,1330,2380, 792, 1,
%e 1, 27, 300,1540,3060,1287, 7,
%e 1, 28, 325,1771,3876,2002, 28,
%p A305556 := proc(n,k)
%p binomial(n-binomial(k,2)-1,k-1) ;
%p end proc:
%p for n from 0 to 30 do
%p for k from 1 to floor((sqrt(1+8*n)-1)/2) do
%p printf("%d,",A305556(n,k)) ;
%p end do:
%p end do:
%Y Cf. A219282 (row sums), A000217 (column 3), A000292 (column 4), A000332 (column 5)
%K nonn,tabf,easy
%O 1,6
%A _R. J. Mathar_, Jun 21 2018
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