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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 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 Cf. A059481, A143418. Sequence in context: A126319 A165553 A056314 * A078631 A160639 A280781 Adjacent sequences:  A171376 A171377 A171378 * A171380 A171381 A171382 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Dec 07 2009 STATUS approved

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Last modified July 24 21:47 EDT 2021. Contains 346273 sequences. (Running on oeis4.)