A202480 Riordan array (1/(1-x), x(2x-1)/(1-x)^2)

1, 1, -1, 1, -1, 1, 1, 0, 1, -1, 1, 2, -1, -1, 1, 1, 5, -5, 2, 1, -1, 1, 9, -10, 8, -3, -1, 1, 1, 14, -14, 14, -11, 4, 1, -1, 1, 20, -14, 14, -17, 14, -5, -1, 1, 1, 27, -6, 0, -9, 19, -17, 6, 1, -1

Offset

0,12

Comments

Row sums are Fibonacci(n-1) = A000045(n-1).

Diagonal sums are A078003(n).

(Sum_{j, 0<=j<=k} T(k,j))/(1-2x)^k gives g.f. of column A165241(n+k-1,k-1) in triangular array in A165241.

Links

Table of n, a(n) for n=0..54.

Formula

T(n,k) = 2*T(n-1,k) + 2*T(n-2,k-1) - T(n-1,k-1) - T(n-2,k).

T(n,k) = (-1)^n*A124341(n,k).

Example

Triangle begins :
1
1, -1
1, -1, 1
1, 0, 1, -1
1, 2, -1, -1, 1
1, 5, -5, 2, 1, -1
1, 9, -10, 8, -3, -1, 1
1, 14, -14, 14, -11, 4, 1, -1
(1+x^2-x^3)/(1-2x)^3 is the g.f of column A165241(n+2,2) := 1, 6, 25, 85, 258, 728, 1952, 5040, ...

Crossrefs

Cf. A000012, A080956, A000045, A078003, A124341, A165241

Sequence in context: A380264 A380266 A146314 * A124341 A275062 A247005

Adjacent sequences: A202477 A202478 A202479 * A202481 A202482 A202483

Keyword

easy,sign,tabl

Author

Philippe Deléham, Dec 20 2011

Status

approved