A167432 Riordan array (c(2x)^2,xc(2x)), c(x) the g.f. of A000108.

1, 4, 1, 20, 6, 1, 112, 36, 8, 1, 672, 224, 56, 10, 1, 4224, 1440, 384, 80, 12, 1, 27456, 9504, 2640, 600, 108, 14, 1, 183040, 64064, 18304, 4400, 880, 140, 16, 1, 1244672, 439296, 128128, 32032, 6864, 1232, 176, 18, 1, 8599552, 3055104, 905216, 232960

Offset: 0

Author

Paul Barry, Nov 03 2009

Keywords

• easy
• nonn
• tabl

Comments

Inverse of (1-4x+4x^2,x(1-2x)) (A167431). Row sums are A084076. First column is A003645.

Examples

			Triangle begins
1,
4, 1,
20, 6, 1,
112, 36, 8, 1,
672, 224, 56, 10, 1,
4224, 1440, 384, 80, 12, 1,
27456, 9504, 2640, 600, 108, 14, 1,
183040, 64064, 18304, 4400, 880, 140, 16, 1,
1244672, 439296, 128128, 32032, 6864, 1232, 176, 18, 1,
8599552, 3055104, 905216, 232960, 52416, 10192, 1664, 216, 20, 1,
60196864, 21498880, 6449664, 1697280, 396032, 81536, 14560, 2184, 260, 22, 1
The production matrix is
4, 1,
4, 2, 1,
8, 4, 2, 1,
16, 8, 4, 2, 1,
32, 16, 8, 4, 2, 1,
64, 32, 16, 8, 4, 2, 1,
128, 64, 32, 16, 8, 4, 2, 1,
256, 128, 64, 32, 16, 8, 4, 2, 1,
512, 256, 128, 64, 32, 16, 8, 4, 2, 1
When topped with the row (1,0,0,0...), this has inverse
1,
-4, 1,
4, -2, 1,
0, 0, -2, 1,
0, 0, 0, -2, 1,
0, 0, 0, 0, -2, 1,
0, 0, 0, 0, 0, -2, 1,
0, 0, 0, 0, 0, 0, -2, 1,
0, 0, 0, 0, 0, 0, 0, -2, 1,
0, 0, 0, 0, 0, 0, 0, 0, -2, 1
		

Formula

Number triangle T(n,k)=A054445(n,k)*2^(n-k).