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 A171379 Triangle sequence of:t(n,k)=A059481(n,k)*(A059481(n,k)-1)/2 0
 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 (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 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; 45, 1485, 24090, 255255, 2003001, 12522510, 65431080, 295475895, 1181927890, 4266801253; MATHEMATICA t[n_, k_] = Binomial[n + k - 1, k]*(Binomial[n + k - 1, k] - 1)/2 Table[Table[t[n, k], {k, 1, n}], {n, 1, 10}] Flatten[%] CROSSREFS Cf. A059481, A143418. Sequence in context: A126319 A165553 A056314 * A078631 A160639 A280781 Adjacent sequences:  A171376 A171377 A171378 * A171380 A171381 A171382 KEYWORD nonn,uned,tabl AUTHOR Roger L. Bagula, Dec 07 2009 STATUS approved

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