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A181089 Triangle T(n,m) = A060821(n,m) + A060821(n,n-m), 0<=m<=n, read by rows. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are 2, 4, 4, -8, -40, -16, 368, 928, -3296,..., 2*A062267(n).

These are the coefficients [x^m] of the polynomial HermiteH(n,x)+ x^n*HermiteH(n,1/x), the sum of the Hermite polynomial of order n and its reverse.

LINKS

Table of n, a(n) for n=0..50.

EXAMPLE

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;

-29216, 0, 279360, 0, -241920, 0, -241920, 0, 279360, 0, -29216;

MATHEMATICA

Clear[p, t, n, m]

p[x_, n_] = HermiteH[n, x] + ExpandAll[x^n*HermiteH[n, 1/x]]

Flatten[Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]]

CROSSREFS

Cf. A060821

Sequence in context: A097033 A268686 A113306 * A171932 A214664 A214666

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 May 23 19:46 EDT 2017. Contains 286926 sequences.