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A096713 Triangle of nonzero coefficients of the modified Hermite polynomials. 4
1, 1, -1, 1, -3, 1, 3, -6, 1, 15, -10, 1, -15, 45, -15, 1, -105, 105, -21, 1, 105, -420, 210, -28, 1, 945, -1260, 378, -36, 1, -945, 4725, -3150, 630, -45, 1, -10395, 17325, -6930, 990, -55, 1, 10395, -62370, 51975, -13860, 1485, -66, 1, 135135, -270270, 135135, -25740, 2145, -78 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Triangle of nonzero coefficients of matching polynomial of complete graph of order n.

Row sums of absolute values produce A000085 (number of involutions). - Wouter Meeussen, Mar 12 2008

REFERENCES

C. D. Godsil, Algebraic Combinatorics, Chapman & Hall, New York, 1993.

LINKS

Table of n, a(n) for n=0..54.

Eric Weisstein's World of Mathematics, Hermite Polynomial

Eric Weisstein's World of Mathematics, Matching Polynomial [From Eric W. Weisstein, Sep 27 2008]

FORMULA

G.f.: HermiteH(n,x/sqrt(2))/2^(n/2). - Wouter Meeussen, Mar 12 2008

EXAMPLE

1, x, -1 + x^2, -3*x + x^3, 3 - 6*x^2 + x^4, 15*x - 10*x^3 + x^5, ...

MATHEMATICA

Table[CoefficientList[HermiteH[n, x/Sqrt[2] ]/2^(n/2), x], {n, 0, 25}] (* Wouter Meeussen, Mar 12 2008 *)

PROG

(PARI) T(n, k)=if(k<0|2*k>n, 0, (-1)^(n\2-k)*n!/(n\2-k)!/(n%2+2*k)!/2^(n\2-k)) /* Michael Somos, Jun 04 2005 */

(Sage)

from sage.functions.hypergeometric import closed_form

def A096713_row(n):

    R.<z> = ZZ[]

    h = hypergeometric([-n/2, (1-n)/2], [], -2*z)

    T = R(closed_form(h)).coefficients()

    return T[::-1]

for n in range(13): A096713_row(n) # Peter Luschny, Aug 21 2014

CROSSREFS

Cf. A000085.

Sequence in context: A055885 A181425 A174505 * A107726 A114159 A236560

Adjacent sequences:  A096710 A096711 A096712 * A096714 A096715 A096716

KEYWORD

sign,tabl

AUTHOR

Eric W. Weisstein, Jul 04 2004

STATUS

approved

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Last modified September 30 09:24 EDT 2014. Contains 247419 sequences.