%I #10 Apr 08 2024 06:57:13

%S 1,1,1,1,5,1,1,13,13,1,1,29,71,29,1,1,61,311,311,61,1,1,125,1205,2435,

%T 1205,125,1,1,253,4313,15653,15653,4313,253,1,1,509,14635,88289,

%U 156259,88289,14635,509,1,1,1021,47875,455275,1310479,1310479,455275,47875

%N Triangle t(n,m) = binomial(n,m) + A008292(n+1,m+1)-1 read by rows.

%C Row sums are 1, 2, 7, 28, 131, 746, 5097, 40440, 363127, 3629302, 39917813,.. = 2^n-n+A033312(n+1).

%F t(n,m) = A007318(n,m)+A008292(n+1,m+1)-1 , 0<=m<=n.

%F t(n,m) = 2*A141689(n+1,m+1)-1. - _R. J. Mathar_, Jan 19 2011

%e 1;

%e 1, 1;

%e 1, 5, 1;

%e 1, 13, 13, 1;

%e 1, 29, 71, 29, 1;

%e 1, 61, 311, 311, 61, 1;

%e 1, 125, 1205, 2435, 1205, 125, 1;

%e 1, 253, 4313, 15653, 15653, 4313, 253, 1;

%e 1, 509, 14635, 88289, 156259, 88289, 14635, 509, 1;

%e 1, 1021, 47875, 455275, 1310479, 1310479, 455275, 47875, 1021, 1;

%e 1, 2045, 152681, 2203607, 9738323, 15724499, 9738323, 2203607, 152681, 2045, 1;

%p A176487 := proc(n,k)

%p binomial(n,k)+A008292(n+1,k+1)-1 ;

%p end proc: # _R. J. Mathar_, Jun 16 2015

%t << DiscreteMath`Combinatorica`;

%t t[n_, m_, 0] := Binomial[n, m];

%t t[n_, m_, 1] := Eulerian[1 + n, m];

%t t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 1] + t[n, m, q - 2] - 1;

%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]

%Y Cf. A007318, A008292

%K nonn,tabl,easy

%O 0,5

%A _Roger L. Bagula_, Apr 19 2010