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A173882 Triangle t(n,m) = A090443(n-1)/(A090443(m-1)*A090443(n-m-1)) read by rows. 1
1, 1, 1, 1, 6, 1, 1, 24, 24, 1, 1, 60, 240, 60, 1, 1, 120, 1200, 1200, 120, 1, 1, 210, 4200, 10500, 4200, 210, 1, 1, 336, 11760, 58800, 58800, 11760, 336, 1, 1, 504, 28224, 246960, 493920, 246960, 28224, 504, 1, 1, 720, 60480, 846720, 2963520, 2963520 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A090443 is defined as +1 at negative indices here, which keeps the definition valid in the range 0 <= m <= n.

Row sums are 1, 2, 8, 50, 362, 2642, 19322, 141794, 1045298, 7742882, 57619982,....

LINKS

Table of n, a(n) for n=0..50.

FORMULA

t(n,0) = t(n,n)=1.

t(n,m) = 2*binomial(n,m)*binomial(n+1,m+1)*binomial(n-1,m-1)*(n-m)/(n-m+1), 0 < m < n.

EXAMPLE

1;

1, 1;

1, 6, 1;

1, 24, 24, 1;

1, 60, 240, 60, 1;

1, 120, 1200, 1200, 120, 1;

1, 210, 4200, 10500, 4200, 210, 1;

1, 336, 11760, 58800, 58800, 11760, 336, 1;

1, 504, 28224, 246960, 493920, 246960, 28224, 504, 1;

1, 720, 60480, 846720, 2963520, 2963520, 846720, 60480, 720, 1;

1, 990, 118800, 2494800, 13970880, 24449040, 13970880, 2494800, 118800, 990, 1;

MAPLE

A090443 := proc(n) (n+2)!*(n+1)!*n!/2 ; end proc:

A173882 := proc(n, m) if m=0 or m= n then 1; else A090443(n-1)/A090443(m-1)/A090443(n-m-1) ; end if; end proc:

seq(seq(A173882(n, m), m=0..n), n=0..5) ; # R. J. Mathar, Mar 19 2011

MATHEMATICA

c[n_] =If[n == 1, 1, If[n == 0, 1, Product[(i - 1)*i*(i + 1), {i, 2, n}]]];

t[n_, m_] = c[n]/(c[m]*c[n - m]);

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Cf. A056939.

Sequence in context: A156139 A309280 A155863 * A174045 A169660 A035348

Adjacent sequences:  A173879 A173880 A173881 * A173883 A173884 A173885

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Mar 01 2010

STATUS

approved

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Last modified July 12 05:35 EDT 2020. Contains 335658 sequences. (Running on oeis4.)