A114164 Riordan array (1/(1-2x), x(1-x)/(1-2x)^2).

1, 2, 1, 4, 5, 1, 8, 18, 8, 1, 16, 56, 41, 11, 1, 32, 160, 170, 73, 14, 1, 64, 432, 620, 377, 114, 17, 1, 128, 1120, 2072, 1666, 704, 164, 20, 1, 256, 2816, 6496, 6608, 3649, 1178, 223, 23, 1, 512, 6912, 19392, 24192, 16722, 7001, 1826, 291, 26, 1, 1024, 16640, 55680, 83232, 69876, 36365, 12235, 2675, 368, 29, 1

Offset: 0

Author

Paul Barry, Nov 15 2005

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A081567. Diagonal sums are A085810. Product of Pascal triangle A007318 and Morgan-Voyce triangle A085478.

Unsigned version of A123876. - Philippe Deléham, Oct 25 2007

Examples

			Triangle begins:
   1;
   2,   1;
   4,   5,   1;
   8,  18,   8,  1;
  16,  56,  41, 11,  1;
  32, 160, 170, 73, 14, 1;
  ...
		

Crossrefs

Cf. A081567, A085810, A007318, A085478, A123876.

T(2n,n) gives A026000.

Formula

Number triangle T(n,k) = Sum_{j=0..n} C(n, j)*C(j+k, 2k);

T(n,k) = Sum_{j=0..n} C(n, k+j)*C(k, k-j)*2^(n-k-j);

T(n,k) = Sum_{j=0..n-k} C(n+k-j, n-k-j)*C(k, j)*(-1)^j*2^(n-k-j).

T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - 4*T(n-2,k) - T(n-2,k-1), T(0,0) = T(1,1) = 1, T(1,0) = 2, T(n,k) = 0 if k < 0 or if k > n. - Philippe Deléham, Jan 17 2014

Extensions

More terms from Michel Marcus, Sep 09 2024