OFFSET
0,2
COMMENTS
Also square array of unsigned coefficients of Hermite polynomials.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10010 (rows 0 to 140, flattened)
FORMULA
T(n,k) = (2n-k)!*2^k/(k!*(n-k)!).
EXAMPLE
Rows begin:
1
2, 2,
12, 12, 4,
120, 120, 48, 8,
1680, 1680, 720, 160, 16,
Unsigned coefficients of Hermite polynomials:
1, 2, 4, 8, ...
2, 12, 48, 160, ...
12, 120, 720, 3360, ...
120, 1680, 13440, 80640, ...
1680, 30240, 302400, 2217600, ...
MAPLE
seq(seq((2*n-k)!*2^k/(k!*(n-k)!), k=0..n), n=0..10); # Robert Israel, Sep 26 2017
MATHEMATICA
y[n_, x_] := Sqrt[2/(Pi*x)]*E^(1/x)*BesselK[-n-1/2, 1/x]; t[n_, k_] := 2^n*Coefficient[y[n, x], x, k]; Table[t[n, k], {n, 0, 8}, {k, n, 0, -1}] // Flatten (* or *) t[n_, k_] := (2*n - k)!*2^k/(k!*(n-k)!); Table[t[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Mar 01 2013 *)
Table[((2n-k)!*2^k)/(k!(n-k)!), {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Nov 23 2017 *)
PROG
(Magma) /* As triangle */ [[Factorial(2*n-k)*2^k/(Factorial(k)*Factorial(n-k)): k in [0..n]]: n in [0.. 10]]; // Vincenzo Librandi, Dec 14 2015
CROSSREFS
KEYWORD
AUTHOR
Philippe Deléham, Aug 12 2005
STATUS
approved