OFFSET
1,3
COMMENTS
Row sums are: {0, 4, 63, 836, 11000, 147757, 2030217, 28435780, 404461170, 5824442504, ...}.
The sequence is the number of connections between figurate numbers A059481 as points page 25 Riordan.
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 25.
LINKS
G. C. Greubel, Rows n = 1..100 of triangle, flattened
FORMULA
T(n,k) = binomial(n+k-1, k)*(binomial(n+k-1, k) - 1)/2.
EXAMPLE
Triangle begins as:
0;
1, 3;
3, 15, 45;
6, 45, 190, 595;
10, 105, 595, 2415, 7875;
15, 210, 1540, 7875, 31626, 106491;
21, 378, 3486, 21945, 106491, 426426, 1471470;
28, 630, 7140, 54285, 313236, 1471470, 5887596, 20701395;
MAPLE
seq(seq( binomial(binomial(n+k-1, k), 2), k=1..n), n=1..10); # G. C. Greubel, Nov 28 2019
MATHEMATICA
Table[Binomial[Binomial[n+k-1, k], 2], {n, 10}, {k, n}]//Flatten (* modified by G. C. Greubel, Nov 28 2019 *)
PROG
(PARI) T(n, k) = binomial(binomial(n+k-1, k), 2); \\ G. C. Greubel, Nov 28 2019
(Magma) [Binomial(Binomial(n+k-1, k), 2): k in [1..n], n in [1..10]]; // G. C. Greubel, Nov 28 2019
(Sage) [[binomial(binomial(n+k-1, k), 2) for k in (1..n)] for n in (1..10)] # G. C. Greubel, Nov 28 2019
(GAP) Flat(List([1..10], n-> List([1..n], k-> Binomial(Binomial(n+k-1, k), 2) ))); # G. C. Greubel, Nov 28 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Dec 07 2009
STATUS
approved