A221179 A convolution triangle of numbers obtained from A146559.

1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, -2, 1, 3, 1, 0, -4, -4, 3, 4, 1, 0, -4, -12, -5, 6, 5, 1, 0, 0, -16, -24, -4, 10, 6, 1, 0, 8, -4, -42, -39, 0, 15, 7, 1, 0, 16, 32, -24, -88, -55, 8, 21, 8, 1, 0, 16, 80, 72, -80

Offset

0,9

Comments

Triangle T(n,k) given by (0, 1, -1, 2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

Links

Table of n, a(n) for n=0..59.

Formula

G.f. for the k-th column: ((x-x^2)/(1-2*x+2*x^2))^k.

G.f.: (1-2*x+2*x^2)/(1-2*x+2*x^2-x*y+x^2*y).

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k) - T(n-2,k-1), T(0,0)=1, T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.

T(n,k) = (-1)^(n-k)*A181472(n-1,k-1) for n>0 and k>0.

T(n,1) = A146559(n-1).

T(n+1,n) = n = A001477(n).

T(n+2,n) = (n^2-n)/2 = A161680(n).

Sum_{k, 0<=k<=n} T(n,k) = A057682(n) for n>0.

Example

Triangle begins:
1
0, 1
0, 1, 1
0, 0, 2, 1
0, -2, 1, 3, 1
0, -4, -4, 3, 4, 1
0, -4, -12, -5, 6, 5, 1
0, 0, -16, -24, -4, 10, 6, 1

Crossrefs

Cf. A030523, A104597, A181472, A220399

Sequence in context: A333211 A258033 A153248 * A341608 A153247 A071432

Adjacent sequences: A221176 A221177 A221178 * A221180 A221181 A221182

Keyword

sign,tabl

Author

Philippe Deléham, Feb 20 2013

Status

approved