OFFSET
0,2
LINKS
G. C. Greubel, Rows n=0..100 of triangle, flattened
E. H. M. Brietzke, An identity of Andrews and a new method for the Riordan array proof of combinatorial identities, Discrete Math., 308 (2008), 4246-4262.
FORMULA
T(n,0) = 4*T(n-1,0) + 5*T(n-1,1) + T(n-1,2), T(n+1,k+1) = T(n,k) + 3*T(n,k+1) + 3*T(n,k+2) + T(n,k+3) for k >= 0.
EXAMPLE
Triangle begins:
1;
4, 1;
21, 7, 1;
120, 45, 10, 1;
715, 286, 78, 13, 1;
4368, 1820, 560, 120, 16, 1;
...
MATHEMATICA
f[n_, k_]:=Binomial[3n+1, 2n+k+1]; Table[ f[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Robert G. Wilson v, May 31 2009 *)
PROG
(PARI) for(n=0, 10, for(k=0, n, print1(binomial(3*n+1, 2*n+k+1), ", "))) \\ G. C. Greubel, May 19 2018
(Magma) /* As triangle */ [[Binomial(3*n+1, 2*n+k+1): k in [0..n]]: n in [0..10]]; // G. C. Greubel, May 19 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Apr 23 2009
EXTENSIONS
More terms from Robert G. Wilson v, May 31 2009
STATUS
approved