OFFSET
1,2
COMMENTS
Row sums are {1, 6, 20, 64, 211, 714, 2430, 8396, 29390, 104004, 371448, 1337216, ...}.
LINKS
G. C. Greubel, Rows n = 1..100 of triangle, flattened
FORMULA
T(n, m) = floor(binomial(n+1, m-1)*binomial(n+2, m-1)/(2*m)).
EXAMPLE
Triangle begins as:
1;
3, 3;
5, 10, 5;
7, 25, 25, 7;
10, 52, 87, 52, 10;
14, 98, 245, 245, 98, 14;
18, 168, 588, 882, 588, 168, 18;
22, 270, 1260, 2646, 2646, 1260, 270, 22;
27, 412, 2475, 6930, 9702, 6930, 2475, 412, 27;
MATHEMATICA
T[n_, k_] = Floor[Binomial[n+1, k]*Binomial[n+2, k]/(2*(k+1))];
Table[T[n, k], {n, 1, 12}, {k, 1, n}]//Flatten (* modified by G. C. Greubel, Apr 13 2019 *)
PROG
(PARI) {T(n, k) = (binomial(n+1, k)*binomial(n+2, k)/(2*k+2))\1};
for(n=1, 12, for(k=1, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Apr 13 2019
(Magma) [[Floor(Binomial(n+1, k)*Binomial(n+2, k)/(2*k+2)): k in [1..n]]: n in [1..12]]; // G. C. Greubel, Apr 13 2019
(Sage) [[floor(binomial(n+1, k)*binomial(n+2, k)/(2*k+2)) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Apr 13 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 07 2010
EXTENSIONS
Partially edited by Jon E. Schoenfield, Dec 02 2013
Edited by G. C. Greubel, Apr 13 2019
STATUS
approved