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A259097
Triangle read by rows: T(n,r) = binomial(n,r)*binomial(2*n-3*r-4,n-2*r-2)/(n-r-1), n >= 2, r = 0..floor(n/2)-1.
1
1, 1, 2, 2, 5, 5, 14, 15, 5, 42, 49, 21, 132, 168, 84, 14, 429, 594, 336, 84, 1430, 2145, 1350, 420, 42, 4862, 7865, 5445, 1980, 330, 16796, 29172, 22022, 9075, 1980, 132, 58786, 109174, 89232, 40898, 10725, 1287, 208012, 411502, 361998, 182182, 55055, 9009, 429, 742900, 1560090, 1469650, 804440, 273273, 55055, 5005
OFFSET
2,3
LINKS
Indranil Ghosh, Rows 2..125, flattened
F. R. Bernhart & N. J. A. Sloane, Emails, April-May 1994
EXAMPLE
Triangle begins:
1;
1;
2, 2;
5, 5;
14, 15, 5;
42, 49, 21;
132, 168, 84, 14;
429, 594, 336, 84;
1430, 2145, 1350, 420, 42;
4862, 7865, 5445, 1980, 330;
16796, 29172, 22022, 9075, 1980, 132;
58786, 109174, 89232, 40898, 10725, 1287;
208012, 411502, 361998, 182182, 55055, 9009, 429;
742900, 1560090, 1469650, 804440, 273273, 55055, 5005;
2674440, 5943200, 5969040, 3527160, 1324960, 312312, 40040, 1430;
...
MAPLE
T:=(n, r) -> binomial(n, r)*binomial(2*n-3*r-4, n-2*r-2)/(n-r-1);
v:=n->[seq(T(n, r), r=0..floor(n/2)-1)];
for n from 2 to 16 do lprint(v(n)); od:
MATHEMATICA
Flatten[Table[Binomial[n, r] Binomial[2n-3r-4, n-2r-2]/(n-r-1), {n, 2, 16}, {r, 0, Floor[(n/2)]-1}]] (* Indranil Ghosh, Feb 20 2017 *)
PROG
(Magma) /* As triangle: */ [[Binomial(n, k)*Binomial(2*n-3*k-4, n-2*k-2)/(n-k-1): k in [0..Floor(n/2)-1]]: n in [2..15]]; // Vincenzo Librandi, Jun 22 2015
CROSSREFS
Row sums are A006343. Right-hand boundary is a mixture of A000108 and A002054.
Sequence in context: A099363 A106181 A098887 * A245845 A097438 A205482
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jun 22 2015
STATUS
approved