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A181089 Triangle T(n, k) = A060821(n,k) + A060821(n,n-k), read by rows. 2
2, 2, 2, 2, 0, 2, 8, -12, -12, 8, 28, 0, -96, 0, 28, 32, 120, -160, -160, 120, 32, -56, 0, 240, 0, 240, 0, -56, 128, -1680, -1344, 3360, 3360, -1344, -1680, 128, 1936, 0, -17024, 0, 26880, 0, -17024, 0, 1936, 512, 30240, -9216, -80640, 48384, 48384, -80640, -9216, 30240, 512 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
T(n, k) = coefficients [x^k] of the polynomial HermiteH(n,x) + x^n*HermiteH(n,1/x).
T(n, k) = A060821(n,k) + A060821(n,n-k).
Sum_{k=0..n} T(n, k) = 2*A062267(n).
EXAMPLE
Triangle begins as:
2;
2, 2;
2, 0, 2;
8, -12, -12, 8;
28, 0, -96, 0, 28;
32, 120, -160, -160, 120, 32;
-56, 0, 240, 0, 240, 0, -56;
128, -1680, -1344, 3360, 3360, -1344, -1680, 128;
1936, 0, -17024, 0, 26880, 0, -17024, 0, 1936;
512, 30240, -9216, -80640, 48384, 48384, -80640, -9216, 30240, 512;
MATHEMATICA
(* First program *)
p[x_, n_] = HermiteH[n, x] + ExpandAll[x^n*HermiteH[n, 1/x]];
Flatten[Table[CoefficientList[p[x, n], x], {n, 0, 15}]] (* edited by G. C. Greubel, Apr 04 2021 *)
(* Second program *)
A060821[n_, k_]:= If[EvenQ[n-k], (-1)^(Floor[(n-k)/2])*2^k*n!/(k!*(Floor[(n - k)/2]!)), 0];
T[n_, k_]:= A060821[n, k] +A060821[n, n-k];
Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Apr 04 2021 *)
PROG
(Sage)
def A060821(n, k): return (-1)^((n-k)//2)*2^k*factorial(n)/(factorial(k)*factorial( (n-k)//2)) if (n-k)%2==0 else 0
def T(n, k): return A060821(n, k) + A060821(n, n-k)
flatten([[T(n, k) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Apr 04 2021
CROSSREFS
Sequence in context: A097033 A268686 A113306 * A341894 A171932 A358094
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula, Oct 02 2010
STATUS
approved

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Last modified June 18 08:27 EDT 2024. Contains 373472 sequences. (Running on oeis4.)