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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
OFFSET
1,2
COMMENTS
Row sums are {1, 6, 20, 64, 211, 714, 2430, 8396, 29390, 104004, 371448, 1337216, ...}.
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 A331925 A252943
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