A176487 Triangle t(n,m) = binomial(n,m) + A008292(n+1,m+1)-1 read by rows.

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, 1205, 125, 1, 1, 253, 4313, 15653, 15653, 4313, 253, 1, 1, 509, 14635, 88289, 156259, 88289, 14635, 509, 1, 1, 1021, 47875, 455275, 1310479, 1310479, 455275, 47875

Offset

0,5

Comments

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

Links

Table of n, a(n) for n=0..52.

Formula

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

t(n,m) = 2*A141689(n+1,m+1)-1. - R. J. Mathar, Jan 19 2011

Example

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, 1205, 125, 1;
1, 253, 4313, 15653, 15653, 4313, 253, 1;
1, 509, 14635, 88289, 156259, 88289, 14635, 509, 1;
1, 1021, 47875, 455275, 1310479, 1310479, 455275, 47875, 1021, 1;
1, 2045, 152681, 2203607, 9738323, 15724499, 9738323, 2203607, 152681, 2045, 1;

Maple

A176487 := proc(n, k)
    binomial(n, k)+A008292(n+1, k+1)-1 ;
end proc: # R. J. Mathar, Jun 16 2015

Mathematica

<< DiscreteMath`Combinatorica`;
t[n_, m_, 0] := Binomial[n, m];
t[n_, m_, 1] := Eulerian[1 + n, m];
t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 1] + t[n, m, q - 2] - 1;
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]

Crossrefs

Cf. A007318, A008292

Sequence in context: A324009 A143007 A152654 * A272644 A157177 A298240

Adjacent sequences: A176484 A176485 A176486 * A176488 A176489 A176490

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Apr 19 2010

Status

approved