OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
T(n,k) = Sum_{i=0..n-k} (binomial(i+k,k)*Sum_{j=0..n-k-i} (binomial(i+j-1,j)*binomial(j,n-k-i-j) )).
Recurrence: T(n+3,k+1) = 2 T(n+2,k+1) + T(n+2,k) + T(n+1,k+1) - T(n+1,k) - T(n,k).
EXAMPLE
Triangle begins:
1;
1, 1;
2, 2, 1;
5, 5, 3, 1;
12, 14, 9, 4, 1;
29, 38, 28, 14, 5, 1;
70, 102, 84, 48, 20, 6, 1;
169, 271, 246, 157, 75, 27, 7, 1;
408, 714, 707, 496, 265, 110, 35, 8, 1;
MATHEMATICA
Flatten[Table[Sum[Binomial[i+k, k]Sum[Binomial[i+j-1, j]Binomial[j, n-k-i-j], {j, 0, n-k-i}], {i, 0, n-k}], {n, 0, 12}, {k, 0, n}]]
PROG
(Maxima) create_list(sum(binomial(i+k, k)*sum(binomial(i+j-1, j)*binomial(j, n-k-i-j), j, 0, n-k-i), i, 0, n-k), n, 0, 12, k, 0, n);
(PARI) for(n=0, 10, for(k=0, n, print1(sum(j=0, n-k, binomial(j+k, k)* sum(r=0, n-k-j, binomial(j+r-1, r)*binomial(r, n-k-j-r))), ", "))) \\ G. C. Greubel, Dec 27 2017
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emanuele Munarini, May 10 2011
STATUS
approved