OFFSET
0,8
COMMENTS
Riordan array (1, x/((1+x)*(1-x)^2)). - Philippe Deléham, Feb 24 2012
Triangle, read by rows, given by (0, 1, 1, -2, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Feb 24 2012
FORMULA
G.f.for column m >= 0: (x/((1-x^2)*(1-x)))^m.
T(n,k) = T(n-1,k-1) + T(n-1,k) + T(n-2,k) - T(n-3,k) with T(n,0) = 0^n. - Philippe Deléham, Feb 24 2012
G.f.: (1-x-x^2+x^3)/(1-x-x^2+x^3-y*x). - Philippe Deléham, Feb 24 2012
Sum_{k, 0<=k<=n} T(n,k)*2^k = A181301(n). - Philippe Deléham, Feb 24 2012
EXAMPLE
{1}; {0,1}; {0,1,1}; {0,2,2,1}; ...
Triangle begins :
1
0, 1
0, 1, 1
0, 2, 2, 1
0, 2, 5, 3, 1
0, 3, 8, 9, 4, 1
0, 3, 14, 19, 14, 5, 1
MATHEMATICA
t[0, 0] = 1; t[_, 0] = 0; t[n_, m_] := Sum[ Sum[ Binomial[j, 2*j-3*k-m+n]*(-1)^(j-k)*Binomial[k, j], {j, 0, k}]*Binomial[m+k-1, m-1], {k, 0, n-m}]; Table[t[n, m], {n, 0, 10}, {m, 0, n}] // Flatten (* Jean-François Alcover, Jun 21 2013 *)
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Apr 06 2001
STATUS
approved