OFFSET
0,2
COMMENTS
For n >= 0, k >= 0 let T(n,k) = sum{i=k..n} binomial(n-k,n-i)*(2i)$ where i$ denotes the swinging factorial of i (A056040). Triangle read by rows.
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.
Peter Luschny, Swinging Factorial.
Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
EXAMPLE
Triangle begins
1;
3, 2;
11, 8, 6;
45, 34, 26, 20;
195, 150, 116, 90, 70;
873, 678, 528, 412, 322, 252;
3989, 3116, 2438, 1910, 1498, 1176, 924;
MAPLE
Computes n rows of the triangle. For the functions 'SumTria' and 'swing' see A163840.
a := n -> SumTria(k->swing(2*k), n, true);
MATHEMATICA
sf[n_] := n!/Quotient[n, 2]!^2; t[n_, k_] := Sum[Binomial[n - k, n - i]*sf[2*i], {i, k, n}]; Table[t[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 28 2013 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Aug 06 2009
STATUS
approved