OFFSET
0,8
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
D. Merlini, D. G. Rogers, R. Sprugnoli and M. C. Verri, On some alternative characterizations of Riordan arrays, Canad J. Math., 49 (1997), 301-320.
FORMULA
G.f.: t*(1+t*z-q)/[(1+t*z)*(2*t^2*z +t*z - 1 + q)], where q = sqrt(1 -2*t*z -3*t^2*z^2).
Sum_{k, 0<=k<=n} T(n,k)*2^(n-k) = A112657(n). - Philippe Deléham, Apr 01 2007
EXAMPLE
Triangle begins
1;
1, 0;
1, 1, 1;
1, 2, 3, 1;
1, 3, 6, 6, 3;
1, 4, 10, 15, 15, 6;
MAPLE
A071947_row := proc(n) local G, k; G := expand((1+x+x^2)^n):
seq(coeff(G, x, k) - coeff(G, x, k-1), k=0..n) end:
seq(print(A071947_row(n)), n=0..11); # Peter Luschny, Oct 01 2014
MATHEMATICA
A027907[n_, k_] := Sum[Binomial[n, j]*Binomial[j, k - j], {j, 0, n}]; A005043[n_] := Sum[(-1)^k*Binomial[n, k]*Binomial[k, Floor[k/2]], {k, 0, n}]; T[n_, k_] := A027907[n, k] - A027907[n, k - 1]; T[n_, n_] := A005043[n]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Mar 02 2017 *)
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Jun 15 2002
EXTENSIONS
Edited by Emeric Deutsch, Mar 04 2004
STATUS
approved