A137388 Triangle t(n,m)= (m^2-1) * binomial(n,m) * (n+2)/(n+2-m) read by rows, 0<=m<=n.

-1, -1, 0, -1, 0, 6, -1, 0, 15, 20, -1, 0, 27, 64, 45, -1, 0, 42, 140, 175, 84, -1, 0, 60, 256, 450, 384, 140, -1, 0, 81, 420, 945, 1134, 735, 216, -1, 0, 105, 640, 1750, 2688, 2450, 1280, 315, -1, 0, 132, 924, 2970, 5544, 6468, 4752, 2079, 440, -1, 0, 162, 1280, 4725, 10368, 14700, 13824, 8505, 3200, 594

Offset

0,6

Comments

Row sums are -1, -1, 5, 34, 135, 440, 1289, 3530, 9227, 23308, 57357, ... = 3 + n - 2^(n+2) + n^2*2^(n-1) + n*2^n.

Links

Table of n, a(n) for n=0..65.

Formula

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

Example

Triangle begins:
  -1;
  -1, 0;
  -1, 0, 6;
  -1, 0, 15, 20;
  -1, 0, 27, 64, 45;
  -1, 0, 42, 140, 175, 84;
  -1, 0, 60, 256, 450, 384, 140;
  -1, 0, 81, 420, 945, 1134, 735, 216;
  -1, 0, 105, 640, 1750, 2688, 2450, 1280, 315;
  -1, 0, 132, 924, 2970, 5544, 6468, 4752, 2079, 440;
  -1, 0, 162, 1280, 4725, 10368, 14700, 13824, 8505, 3200, 594;

Maple

A137388 := proc(n, m)
        (m^2-1)*binomial(n, m)*(n+2)/(n+2-m) ;
end proc:
seq(seq(A137388(n, m), m=0..n), n=0..14) ; # R. J. Mathar, Nov 10 2011

Mathematica

a0 = Table[Table[(n - 1)*(n + 1)*Binomial[m, n]*Binomial[m + 2, n]/Binomial[m + 1, n], {n, 0, m}], {m, 0, 10}]; Flatten[a0]

Crossrefs

Sequence in context: A204013 A127573 A351110 * A302971 A114153 A119832

Adjacent sequences: A137385 A137386 A137387 * A137389 A137390 A137391

Keyword

tabl,sign,easy

Author

Roger L. Bagula and Gary W. Adamson, Apr 10 2008

Status

approved