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A112333 An invertible triangle of ratios of triple factorials. 5
1, 2, 1, 10, 5, 1, 80, 40, 8, 1, 880, 440, 88, 11, 1, 12320, 6160, 1232, 154, 14, 1, 209440, 104720, 20944, 2618, 238, 17, 1, 4188800, 2094400, 418880, 52360, 4760, 340, 20, 1, 96342400, 48171200, 9634240, 1204280, 109480, 7820, 460, 23, 1, 2504902400 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First column is A008544. Second column is A034000. Third column is A051605. As a square array read by antidiagonals, columns have e.g.f. (1/(1-3x)^(2/3)) * (1/(1-3x))^k.

LINKS

Table of n, a(n) for n=0..45.

FORMULA

Number triangle T(n, k)=if(k<=n, Product{k=1..n, 3k-1}/Product{j=1..k, 3j-1}, 0); T(n, k)=if(k<=n, 3^(n-k)*(n-1/3)!/(k-1/3)!, 0).

EXAMPLE

Triangle begins

      1;

      2,    1;

     10,    5,    1;

     80,   40,    8,   1;

    880,  440,   88,  11,  1;

  12320, 6160, 1232, 154, 14, 1;

Inverse triangle A112334 begins

   1;

  -2,  1;

   0, -5,  1;

   0,  0, -8,   1;

   0,  0,  0, -11,   1;

   0,  0,  0,   0, -14,   1;

   0,  0,  0,   0,   0, -17, 1;

MAPLE

nmax:=8: for n from 0 to nmax do for k from 0 to n do if k<=n then T(n, k) := mul(3*k1-1, k1=1..n)/ mul(3*j-1, j=1..k) else T(n, k) := 0: fi: od: od: for n from 0 to nmax do seq(T(n, k), k=0..n) od: seq(seq(T(n, k), k=0..n), n=0..nmax); # Johannes W. Meijer, Jul 04 2011, revised Nov 23 2012

CROSSREFS

Sequence in context: A121334 A126450 A235608 * A066868 A193900 A319373

Adjacent sequences:  A112330 A112331 A112332 * A112334 A112335 A112336

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Sep 04 2005

STATUS

approved

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Last modified August 25 10:46 EDT 2019. Contains 326324 sequences. (Running on oeis4.)