OFFSET
0,5
COMMENTS
Row sums are 1, 2, 8, 48, 408, 5296, 113200, 4105184, 255805472, 27442457664, 5089653253824, ... = 2*A006117(n)-2^n.
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
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula and Gary W. Adamson, Mar 21 2010
STATUS
approved