A118244 Triangle, rows = inverse binomial transforms of sequences generated from the Pell polynomials.

1, 2, 1, 5, 5, 2, 12, 21, 18, 6, 29, 80, 116, 84, 24, 70, 290, 642, 774, 480, 120

Offset: 0

Author

Gary W. Adamson, Apr 17 2006

Keywords

• nonn
• tabl

Comments

Columns of A118243 are f(x), the Pell polynomials. (terms of A038137 considered as Pell polynomial coefficients): 1; (x + 1); (x^2 + 2x + 2); (x^3 + 3x^2 + 5x + 3); (x^4 + 4x^3 + 9x^2 + 10x + 5);...For example, (x^3 + 3x^2 + 5x + 3), (f(x), x=1,2,3...), generates column 3 of triangle A118243: (12, 33, 72, 135, 228, 357...); and the inverse binomial transform of (12, 33, 72...) = row 3 of the triangle: (12, 21, 18, 6). The array of A118243 is obtained by deleting the Fibonacci sequence (first row of the A073133 array).

Examples

			Row 3 of the triangle = (5, 5, 2), = inverse binomial transform of column 3 of A118243: (5, 10, 17, 26, 37...). Example: 17 = 1*2 + 1*5 + 2*5 = 2 + 5 + 10.
First few rows of the triangle are:
1;
2, 1;
5, 5, 2;
12, 21, 18, 6;
29, 80, 116, 84, 24;
70, 290, 642, 774, 480, 120;
...
		

Crossrefs

Cf. A038137, A118243, A073133.

Formula

n-th row of the triangle = inverse binomial transform of n-th column of A118243.