login
A174346
Triangle T(n, k) = (binomial(n-1, k-1)*binomial(n, k-1)/k) * ( 3^(k-1) if floor(n/2) >= k, otherwise 3^(n-k) ), read by rows.
1
1, 1, 1, 1, 9, 1, 1, 18, 18, 1, 1, 30, 180, 30, 1, 1, 45, 450, 450, 45, 1, 1, 63, 945, 4725, 945, 63, 1, 1, 84, 1764, 13230, 13230, 1764, 84, 1, 1, 108, 3024, 31752, 142884, 31752, 3024, 108, 1, 1, 135, 4860, 68040, 428652, 428652, 68040, 4860, 135, 1
OFFSET
1,5
FORMULA
T(n, k) = (binomial(n-1, k-1)*binomial(n, k-1)/k) * ( 3^(k-1) if floor(n/2) >= k, otherwise 3^(n-k) ).
T(n, n-k) = T(n, k).
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 9, 1;
1, 18, 18, 1;
1, 30, 180, 30, 1;
1, 45, 450, 450, 45, 1;
1, 63, 945, 4725, 945, 63, 1;
1, 84, 1764, 13230, 13230, 1764, 84, 1;
1, 108, 3024, 31752, 142884, 31752, 3024, 108, 1;
1, 135, 4860, 68040, 428652, 428652, 68040, 4860, 135, 1;
MATHEMATICA
T[n_, k_]:= (Binomial[n-1, k-1]*Binomial[n, k-1]/k)*If[Floor[n/2]>k-1, 3^(k-1), 3^(n-k)];
Table[T[n, k], {n, 12}, {k, n}]//Flatten
PROG
(Magma)
function T(n, k)
if Floor(n/2) gt k-1 then return (1/n)*Binomial(n, k)*Binomial(n, k-1)*3^(k-1);
else return (1/n)*Binomial(n, k)*Binomial(n, k-1)*3^(n-k);
end if; return T;
end function;
[T(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Nov 26 2021
(Sage)
def A174346(n, k): return (1/n)*binomial(n, k)*binomial(n, k-1)*( 3^(k-1) if ((n//2)>k-1) else 3^(n-k) )
flatten([[A174346(n, k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Nov 26 2021
CROSSREFS
Cf. A081582.
Sequence in context: A168625 A143681 A081582 * A144404 A014761 A073702
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 16 2010
EXTENSIONS
Edited by G. C. Greubel, Nov 26 2021
STATUS
approved