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

0,5

Comments

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

Links

Table of n, a(n) for n=0..47.

Example

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;

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}]

Crossrefs

Cf. A060187.

Sequence in context: A152969 A138076 A060187 * A156139 A309280 A155863

Adjacent sequences: A174524 A174525 A174526 * A174528 A174529 A174530

Keyword

nonn,tabl

Author

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

Status

approved