OFFSET
0,2
COMMENTS
Row sums = A048487: (1, 6, 16, 36, 76, 156, ...).
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
FORMULA
Bivariate o.g.f.: Sum_{n,k>=0} T(n,k)*x^n*y^k = (1 + 4*x - x*y)/((1 - x*y)*(1 - x - x*y)). - Petros Hadjicostas, Feb 20 2021
EXAMPLE
Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
1;
5, 1;
5, 10, 1;
5, 15, 15, 1;
5, 20, 30, 20, 1;
5, 25, 50, 50, 25, 1;
5, 30, 75, 100, 75, 30, 1;
...
MAPLE
seq(seq(`if`(k=n, 1, 5*binomial(n, k)), k=0..n), n=0..10); # G. C. Greubel, Nov 18 2019
MATHEMATICA
Table[If[k==n, 1, 5*Binomial[n, k]], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 18 2019 *)
PROG
(PARI) T(n, k) = if(k==n, 1, 5*binomial(n, k)); \\ G. C. Greubel, Nov 18 2019
(Magma) [k eq n select 1 else 5*Binomial(n, k): k in [0..n], n in [0..10]]; // G. C. Greubel, Nov 18 2019
(Sage)
def T(n, k):
if k == n: return 1
else: return 5*binomial(n, k)
[[T(n, k) for k in (0..n)] for n in (0..10)]
# G. C. Greubel, Nov 18 2019
(GAP)
T:= function(n, k)
if k=n then return 1;
else return 5*Binomial(n, k);
fi; end;
Flat(List([0..10], n-> List([0..n], k-> T(n, k) ))); # G. C. Greubel, Nov 18 2019
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Jun 15 2007
STATUS
approved