A157491 A050165*A130595 as infinite lower triangular matrices.

1, 0, 1, 0, -1, 2, 0, 2, -6, 5, 0, -5, 20, -28, 14, 0, 14, -70, 135, -120, 42, 0, -42, 252, -616, 770, -495, 132, 0, 132, -924, 2730, -4368, 4004, -2002, 429, 0, -429, 3432, -11880, 23100, -27300, 19656, -8008, 1430

Offset: 0

Author

Philippe Deléham, Mar 01 2009

Keywords

• sign
• tabl

Comments

Triangle, read by rows, given by [0,-1,-1,-1,-1,-1,-1,...] DELTA [1,1,1,1,1,1,1,1,...] where DELTA is the operator defined in A084938. Triangle related to k-regular trees.

Examples

			Triangle begins:
  1;
  0,  1;
  0, -1,  2;
  0,  2, -6,   5;
  0, -5, 20, -28, 14;
  ...
		

Links

• Paul Barry, A Note on a Family of Generalized Pascal Matrices Defined by Riordan Arrays, Journal of Integer Sequences, 16 (2013), #13.5.4.
• Jian Zhou, On Some Mathematics Related to the Interpolating Statistics, arXiv:2108.10514 [math-ph], 2021.

Crossrefs

Cf. A000108, A062991, A094385.

Formula

Sum_{k=0..n} T(n,k)*x^k = A000007(n), A000012(n), A000984(n), A089022(n), A035610(n), A130976(n), A130977(n), A130978(n), A130979(n), A130980(n), A131521(n) for x = 0,1,2,3,4,5,6,7,8,9,10 respectively.

Sum_{k=0..n} T(n,k)*x^(n-k) = A064093, A064092, A064091, A064090, A064089, A064088, A064087, A064063, A064062, A000108, A000012, A064310, A064311, A064325, A064326, A064327, A064328, A064329, A064330, A064331, A064332, A064333 for x = -9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,12 respectively. [Philippe Deléham, Mar 03 2009]