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 A174102 Triangle read by rows: T(n, m) = floor(binomial(n+1, m)* binomial(n+2, m)/(2*m+2)), 1 <= m <= n. 2
 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, 33, 605, 4537, 16335, 30492, 30492, 16335, 4537, 605, 33 (list; table; graph; refs; listen; history; text; internal format)
 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 Cf. A166454. Cf. A011848 (right diagonal). Sequence in context: A202674 A027170 A132775 * A217521 A252943 A294617 Adjacent sequences:  A174099 A174100 A174101 * A174103 A174104 A174105 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

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Last modified January 25 01:42 EST 2020. Contains 331229 sequences. (Running on oeis4.)