A091595 Triangle read by rows: T(n,m) := Sum_{k=0..floor((n-m)/2)} binomial(n-2k,m) * binomial(n-m-k,k) * 2^k.

1, 1, 1, 3, 2, 1, 5, 5, 3, 1, 11, 12, 8, 4, 1, 21, 27, 22, 12, 5, 1, 43, 62, 55, 36, 17, 6, 1, 85, 137, 137, 99, 55, 23, 7, 1, 171, 304, 330, 264, 164, 80, 30, 8, 1, 341, 663, 784, 682, 466, 256, 112, 38, 9, 1, 683, 1442, 1833, 1720, 1278, 772, 382, 152, 47, 10, 1, 1365, 3109, 4235, 4257, 3402, 2234, 1218, 550, 201, 57, 11, 1

Offset: 0

Author

Paul Barry, Jan 23 2004

Keywords

• easy
• nonn
• tabl

Comments

A Jacobsthal related number number triangle.

Examples

			Rows begin:
   1,
   1,   1,
   3,   2,   1,
   5,   5,   3,  1,
  11,  12,   8,  4,  1,
  21,  27,  22, 12,  5,  1,
  43,  62,  55, 36, 17,  6, 1,
  85, 137, 137, 99, 55, 23, 7, 1,
  ...
		

Links

• Seiichi Manyama, Rows n = 0..139, flattened

Crossrefs

Columns include A001045, A091596. Row sums are A077937.

Formula

k-th column has g.f. 1/(1-x-2x^2) * ( x*(1-2x^2)/(1-x-2x^2) )^k.