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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

Table of n, a(n) for n=0..40.

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 November 19 14:52 EST 2018. Contains 317352 sequences. (Running on oeis4.)