A171567 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A168491.

1, -1, 1, 2, -2, 1, -5, 5, -3, 1, 14, -14, 9, -4, 1, -42, 42, -28, 14, -5, 1, 132, -132, 90, -48, 20, -6, 1, -429, 429, -297, 165, -75, 27, -7, 1, 1430, -1430, 1001, -572, 275, -110, 35, -8, 1, -4862, 4862, -3432, 2002, -1001, 429, -154, 44, -9, 1

Offset

0,4

Comments

Equal to B^(-2)*A054336, B = A007318. T(n,0)=(-1)^n*A000108(n). Unsigned version in A033184.

Links

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

Formula

T(n,k) = (-1)^(n-k)*(k+1)*binomial(2n-k, n-k)/(n+1), 0<=k<=n; else 0.

T(n,k) = T(n-1,k-1) - T(n-1,k) + sum_{i, i>=0} T(n-1,k+1+i)*(-1)^i. - Philippe Deléham, Feb 23 2012

Example

Triangle begins : 1 ; -1,1 ; 2,-2,1 ; -5,5,-3,1 ; 14,-14,9,-4,1 ;...

Crossrefs

Cf. A033184, A171488, A054336, A154930

Sequence in context: A141751 A079222 A033184 * A110488 A271025 A134379

Adjacent sequences: A171564 A171565 A171566 * A171568 A171569 A171570

Keyword

sign,tabl

Author

Philippe Deléham, Dec 11 2009

Status

approved