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A174527
Triangle T(n,m) = 2*A022167(n,m) - binomial(n, m), 0 <= m <= n, read by rows.
1
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.
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 A060187 A138076 * A156139 A309280 A155863
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved