A174526 Triangle t(n,m) = 2*A022166(n,m)-binomial(n,m), read by rows, 0<=m<=n.

1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 26, 64, 26, 1, 1, 57, 300, 300, 57, 1, 1, 120, 1287, 2770, 1287, 120, 1, 1, 247, 5313, 23587, 23587, 5313, 247, 1, 1, 502, 21562, 194254, 401504, 194254, 21562, 502, 1, 1, 1013, 86834, 1575986, 6619368, 6619368, 1575986, 86834

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Mar 21 2010

Keywords

• nonn
• tabl

Comments

Row sums are 1, 2, 6, 24, 118, 716, 5586, 58296, 834142, 16566404, 459510186,... = 2*A006116(n)-2^n.

The column m=1 might be A000295. - R. J. Mathar, Nov 14 2011

Examples

			1;
1, 1;
1, 4, 1;
1, 11, 11, 1;
1, 26, 64, 26, 1;
1, 57, 300, 300, 57, 1;
1, 120, 1287, 2770, 1287, 120, 1;
1, 247, 5313, 23587, 23587, 5313, 247, 1;
1, 502, 21562, 194254, 401504, 194254, 21562, 502, 1;
1, 1013, 86834, 1575986, 6619368, 6619368, 1575986, 86834, 1013, 1;
1, 2036, 348457, 12695310, 107487764, 218443050, 107487764, 12695310, 348457, 2036, 1;
		

Crossrefs

Cf. A008292.

Programs

Maple

A174526 := proc(n,k)
   2*A022166(n,k)-binomial(n,k) ;
end proc:
seq(seq(A174526(n,m),m=0..n),n=0..10) ; # R. J. Mathar, Nov 14 2011

Mathematica

c[n_, q_] = Product[1 - q^i, {i, 1, n}];
t[n_, m_, q_] = 2*c[n, q]/(c[m, q]*c[n - m, q]) - Binomial[n, m];
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]
(* second program: *)
t[n_, m_] := 2 QBinomial[n, m, 2] - Binomial[n, m]; Table[t[n, m], {n, 0, 10}, {m, 0, n}] // Flatten (* Jean-François Alcover, Apr 09 2016 *)