OFFSET
0,5
COMMENTS
Row sums are 1, 2, 10, 80, 1042, 24524, 1131382, 102819584, 18742118986, 6775774063892, 4926666912583390, ... = 2*A006118(n) - 2^n.
This triangle essentially compares a Gaussian binomial equivalent to Pascal's triangle and Pascal's triangle itself. - Alonso del Arte, Nov 14 2011
EXAMPLE
Triangle begins
1;
1, 1;
1, 8, 1;
1, 39, 39, 1;
1, 166, 708, 166, 1;
1, 677, 11584, 11584, 677, 1;
1, 2724, 186171, 753590, 186171, 2724, 1;
1, 10915, 2981685, 48417191, 48417191, 2981685, 10915, 1;
1, 43682, 47718190, 3101684114, 12443227012, 3101684114, 47718190, 43682, 1;
MAPLE
A174528 := proc(n, k)
2*A022168(n, k)-binomial(n, k) ;
end proc:
seq(seq(A174528(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}]
(* alternate program *)
(* First run the program for A022168 to define gaussianBinom *)
Column[Table[2gaussianBinom[n, k, 4] - Binomial[n, k], {n, 0, 8}, {k, 0, n}], Center] (* Alonso del Arte, Nov 14 2011 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula and Gary W. Adamson, Mar 21 2010
STATUS
approved