A105848 Binomial transform of number triangle A105632.

1, 2, 1, 5, 3, 1, 14, 9, 4, 1, 42, 29, 14, 5, 1, 132, 99, 50, 20, 6, 1, 429, 351, 186, 78, 27, 7, 1, 1430, 1275, 714, 311, 114, 35, 8, 1, 4862, 4707, 2796, 1271, 483, 159, 44, 9, 1, 16796, 17577, 11082, 5282, 2082, 712, 214, 54, 10, 1, 58786, 66197, 44250, 22160

Offset: 0

Author

Paul Barry, Apr 22 2005

Keywords

• easy
• nonn
• tabl

Comments

Product of binomial matrix C(n,k) and A105632. Row sums are A105849.

Examples

			Triangle begins
1;
2,1;
5,3,1;
14,9,4,1;
42,29,14,5,1;
132,99,50,20,6,1;
		

Formula

Column k has g.f. (sum{j=0..k-1, C(k-1, j)C(j)x^(2j)/(1-4x)^(j+1/2)}+0^k*(1-2x-sqrt(1-4x))/(2x^2))(x/(1-x))^k