OFFSET
0,5
COMMENTS
Row sums = A131064: (1, 2, 8, 24, 60, 136, 292, ...), the binomial transform of (1, 1, 5, 5, 5, ...).
LINKS
Muniru A Asiru, Rows n=0..100 of triangle, flattened
FORMULA
G.f.: (1-z-t*z+5*t*z^2)/((1-z)*(1-t*z)*(1-z-t*z)). - Emeric Deutsch, Jun 20 2007
EXAMPLE
First few rows of the triangle:
1;
1, 1;
1, 6, 1;
1, 11, 11, 1;
1, 16, 26, 16, 1;
1, 21, 46, 46, 21, 1;
1, 26, 71, 96, 71, 26, 1;
...
MAPLE
T := proc (n, k) if k <= n then 5*binomial(n, k)-4 else 0 end if end proc: for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # Emeric Deutsch, Jun 20 2007
MATHEMATICA
Table[5*Binomial[n, k] -4, {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Mar 12 2020 *)
PROG
(GAP) Print(Flat(List([0..10], n->List([0..n], k->5*Binomial(n, k)-4)))); # Muniru A Asiru, Feb 21 2019
(Magma) [5*Binomial(n, k) -4: k in [0..n], n in [0..10]]; // G. C. Greubel, Mar 12 2020
(Sage) [[5*binomial(n, k) -4 for k in (0..n)] for n in (0..10)] # G. C. Greubel, Mar 12 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 13 2007
EXTENSIONS
More terms from Emeric Deutsch, Jun 20 2007
STATUS
approved