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%I #19 Jan 18 2022 13:25:22
%S 1,0,1,0,-1,2,0,2,-6,5,0,-5,20,-28,14,0,14,-70,135,-120,42,0,-42,252,
%T -616,770,-495,132,0,132,-924,2730,-4368,4004,-2002,429,0,-429,3432,
%U -11880,23100,-27300,19656,-8008,1430
%N A050165*A130595 as infinite lower triangular matrices.
%C 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.
%H Paul Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Barry2/barry231.html">A Note on a Family of Generalized Pascal Matrices Defined by Riordan Arrays</a>, Journal of Integer Sequences, 16 (2013), #13.5.4.
%H Jian Zhou, <a href="https://arxiv.org/abs/2108.10514">On Some Mathematics Related to the Interpolating Statistics</a>, arXiv:2108.10514 [math-ph], 2021.
%F 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.
%F 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]
%e Triangle begins:
%e 1;
%e 0, 1;
%e 0, -1, 2;
%e 0, 2, -6, 5;
%e 0, -5, 20, -28, 14;
%e ...
%Y Cf. A000108, A062991, A094385.
%K sign,tabl
%O 0,6
%A _Philippe Deléham_, Mar 01 2009
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