A112333 An invertible triangle of ratios of triple factorials.

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

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