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 A156914 Triangle sequence of the central q-binomial as an antidiagonal: t(n,m)=q-binomial(2*n,n,m+1). 0
 1, 1, 2, 1, 3, 6, 1, 4, 35, 20, 1, 5, 130, 1395, 70, 1, 6, 357, 33880, 200787, 252, 1, 7, 806, 376805, 75913222, 109221651, 924, 1, 8, 1591, 2558556, 6221613541, 1506472167928, 230674393235, 3432, 1, 9, 2850, 12485095, 200525284806 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums are: {1, 3, 10, 60, 1601, 235283, 185513416, 1743370738292, 271152216368521131, 433949978891501890005203, 6589541880665684362990682314774,...} LINKS FORMULA t(n,m)=q-binomial(2*n,n,m+1); out(n,m)=antidiagonal(t(n,m)). EXAMPLE {1}, {1, 2}, {1, 3, 6}, {1, 4, 35, 20}, {1, 5, 130, 1395, 70}, {1, 6, 357, 33880, 200787, 252}, {1, 7, 806, 376805, 75913222, 109221651, 924}, {1, 8, 1591, 2558556, 6221613541, 1506472167928, 230674393235, 3432}, {1, 9, 2850, 12485095, 200525284806, 1634141006295525, 267598665689058580, 1919209135381395, 12870}, {1, 10, 4745, 48177200, 3500412775495, 391901483074853556, 6857430062381149327845, 427028776969176679964080, 63379954960524853651, 48620}, {1, 11, 7462, 156087945, 39709010932102, 35285166561510069127, 19138263752352528498478556, 460250514083576206796548772325, 6129263888495201102915629695046, 8339787869494479328087443, 184756} MATHEMATICA Clear[t, n, m, i, k, c, d, b]; t[n_, m_] = If[m == 0, n!, Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]; c = Table[Table[b[2*n, n, m], {n, 0, 10}], {m, 0, 10}]; d = Table[Table[c[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[c]}]; Flatten[d] CROSSREFS A000984, A022166, A022167, A022168, A022169, A022170, A022171, A022175. Sequence in context: A120257 A059298 A214306 * A289656 A248686 A059434 Adjacent sequences:  A156911 A156912 A156913 * A156915 A156916 A156917 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 18 2009 STATUS approved

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Last modified October 15 00:04 EDT 2019. Contains 328025 sequences. (Running on oeis4.)