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 A174526 Triangle t(n,m) = 2*A022166(n,m)-binomial(n,m), read by rows, 0<=m<=n. 1
 1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 26, 64, 26, 1, 1, 57, 300, 300, 57, 1, 1, 120, 1287, 2770, 1287, 120, 1, 1, 247, 5313, 23587, 23587, 5313, 247, 1, 1, 502, 21562, 194254, 401504, 194254, 21562, 502, 1, 1, 1013, 86834, 1575986, 6619368, 6619368, 1575986, 86834 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are 1, 2, 6, 24, 118, 716, 5586, 58296, 834142, 16566404, 459510186,... = 2*A006116(n)-2^n. The column m=1 might be A000295. - R. J. Mathar, Nov 14 2011 LINKS EXAMPLE 1; 1, 1; 1, 4, 1; 1, 11, 11, 1; 1, 26, 64, 26, 1; 1, 57, 300, 300, 57, 1; 1, 120, 1287, 2770, 1287, 120, 1; 1, 247, 5313, 23587, 23587, 5313, 247, 1; 1, 502, 21562, 194254, 401504, 194254, 21562, 502, 1; 1, 1013, 86834, 1575986, 6619368, 6619368, 1575986, 86834, 1013, 1; 1, 2036, 348457, 12695310, 107487764, 218443050, 107487764, 12695310, 348457, 2036, 1; MAPLE A174526 := proc(n, k)    2*A022166(n, k)-binomial(n, k) ; end proc: seq(seq(A174526(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}] (* second program: *) t[n_, m_] := 2 QBinomial[n, m, 2] - Binomial[n, m]; Table[t[n, m], {n, 0, 10}, {m, 0, n}] // Flatten (* Jean-François Alcover, Apr 09 2016 *) CROSSREFS Cf. A008292. Sequence in context: A168287 A221987 A285357 * A008292 A174036 A157221 Adjacent sequences:  A174523 A174524 A174525 * A174527 A174528 A174529 KEYWORD nonn,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Mar 21 2010 STATUS approved

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Last modified August 4 08:25 EDT 2020. Contains 336201 sequences. (Running on oeis4.)