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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

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

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

Cf. A060821, A062267.

Sequence in context: A097033 A268686 A113306 * A341894 A171932 A305629

Adjacent sequences:  A181086 A181087 A181088 * A181090 A181091 A181092

KEYWORD

sign,tabl

AUTHOR

Roger L. Bagula, Oct 02 2010

STATUS

approved

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Last modified June 24 18:46 EDT 2021. Contains 345419 sequences. (Running on oeis4.)