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A171379 Triangle, read by rows, T(n, k) = A059481(n,k)*(A059481(n,k) - 1)/2. 1
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, 36, 990, 13530, 122265, 827541, 4507503, 20701395, 82812015, 295475895 (list; table; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A126319 A165553 A056314 * A078631 A352802 A160639
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Dec 07 2009
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)