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

0,2

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).

Links

Table of n, a(n) for n=0..20.

Formula

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

Example

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.

Sequence in context: A204119 A046757 A248905 * A108410 A058116 A058118

Adjacent sequences: A118241 A118242 A118243 * A118245 A118246 A118247

Keyword

nonn,tabl

Author

Gary W. Adamson, Apr 17 2006

Status

approved