OFFSET
0,2
COMMENTS
Triangle read by rows. For n >= 0, k >= 0 let
T(n,k) = sum{i=k..n} binomial(n-k,n-i)*(2i+1)$
where i$ denotes the swinging factorial of i (A056040).
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.
EXAMPLE
1
7, 6
43, 36, 30
249, 206, 170, 140
1395, 1146, 940, 770, 630
7653, 6258, 5112, 4172, 3402, 2772
41381, 33728, 27470, 22358, 18186, 14784, 12012
MAPLE
Computes n rows of the triangle. For the functions 'SumTria' and 'swing' see A163840.
a := n -> SumTria(k->swing(2*k+1), n, true);
MATHEMATICA
sf[n_] := n!/Quotient[n, 2]!^2; t[n_, k_] := Sum[Binomial[n-k, n-i]*sf[2*i+1], {i, k, n}]; Table[t[n, k], {n, 0, 7}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 28 2013 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Aug 06 2009
STATUS
approved