OFFSET
0,4
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
Riordan array (1/sqrt(1-2*x-3*x^2), (1-x-2*x^2-sqrt(1-2*x-3*x^2) ) / (2*x^2)).
Number triangle T(n,k) = Sum_{j=0..n} C(n,j-k)*C(j,n-j).
EXAMPLE
Triangle begins
1,
1, 1,
3, 3, 1,
7, 9, 5, 1,
19, 26, 19, 7, 1,
51, 75, 65, 33, 9, 1,
141, 216, 211, 132, 51, 11, 1
MATHEMATICA
T[n_, k_] := Sum[Binomial[n, j - k]*Binomial[j, n - j], {j, 0, n}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Feb 28 2017 *)
PROG
(PARI) {T(n, k) = sum(j=0, n, binomial(n, j-k)*binomial(j, n-j))};
for(n=0, 10, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Dec 15 2018
(Magma) [[(&+[Binomial(n, j-k)*Binomial(j, n-j): j in [0..n]]): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Dec 15 2018
(Sage) [[sum(binomial(n, j-k)*binomial(j, n-j) for j in range(n+1)) for k in range(n+1)] for n in range(10)] # G. C. Greubel, Dec 15 2018
(GAP) T:=Flat(List([0..10], n->List([0..n], k->Sum([0..n], j-> Binomial(n, j-k)*Binomial(j, n-j))))); # G. C. Greubel, Dec 15 2018
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Feb 12 2006
STATUS
approved