A174527 Triangle T(n,m) = 2*A022167(n,m) - binomial(n, m), 0 <= m <= n, read by rows.

1, 1, 1, 1, 6, 1, 1, 23, 23, 1, 1, 76, 254, 76, 1, 1, 237, 2410, 2410, 237, 1, 1, 722, 22007, 67740, 22007, 722, 1, 1, 2179, 198905, 1851507, 1851507, 198905, 2179, 1, 1, 6552, 1792492, 50190504, 151826374, 50190504, 1792492, 6552, 1, 1, 19673, 16139204

Offset: 0

Author

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

Keywords

• nonn
• tabl

Comments

Row sums are 1, 2, 8, 48, 408, 5296, 113200, 4105184, 255805472, 27442457664, 5089653253824, ... = 2*A006117(n)-2^n.

Examples

			Triangle begins
  1;
  1,    1;
  1,    6,       1;
  1,   23,      23,        1;
  1,   76,     254,       76,         1;
  1,  237,    2410,     2410,       237,        1;
  1,  722,   22007,    67740,     22007,      722,       1;
  1, 2179,  198905,  1851507,   1851507,   198905,    2179,    1;
  1, 6552, 1792492, 50190504, 151826374, 50190504, 1792492, 6552, 1;
		

Crossrefs

Cf. A060187.

Programs

Maple

A174527 := proc(n,k)
        2*A022167(n,k)-binomial(n,k) ;
end proc:
seq(seq(A174527(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}]