A172250 Triangle, read by rows, given by [0,1,-1,0,0,0,0,0,0,0,...] DELTA [1,-1,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

1, 0, 1, 0, 1, 0, 0, 0, 2, -1, 0, 0, 1, 1, -1, 0, 0, 0, 3, -2, 0, 0, 0, 0, 1, 3, -4, 1, 0, 0, 0, 0, 4, -2, -2, 1, 0, 0, 0, 0, 1, 6, -9, 3, 0, 0, 0, 0, 0, 0, 5, 0, -9, 6, -1, 0, 0, 0, 0, 0, 1, 10, -15, 3, 3, -1, 0, 0, 0, 0, 0, 0, 6, 5, -24, 18, -4, 0, 0, 0, 0, 0, 0, 0, 1, 15, -20, -6, 18, -8, 1

Offset

0,9

Links

Table of n, a(n) for n=0..90.

Formula

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

Sum_{k=0..n} T(n,k)*x^k = (-1)^n*A088139(n+1), A001607(n+1), A000007(n), A000012(n), A099087(n), A190960(n+1) for x = -2, -1, 0, 1, 2, 3 respectively. - Philippe Deléham, Feb 15 2012

G.f.: 1/(1-y*x+y*(y-1)*x^2). - Philippe Deléham, Feb 15 2012

Example

Triangle begins:
  1;
  0,  1;
  0,  1,  0;
  0,  0,  2, -1;
  0,  0,  1,  1, -1;
  0,  0,  0,  3, -2,  0;
  0,  0,  0,  1,  3, -4,  1;
  0,  0,  0,  0,  4, -2, -2,  1; ...

Crossrefs

Cf. A101950.

Sequence in context: A115201 A354100 A118229 * A309047 A255317 A309168

Adjacent sequences: A172247 A172248 A172249 * A172251 A172252 A172253

Keyword

sign,tabl

Author

Philippe Deléham, Jan 29 2010

Status

approved