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A079949 Special values of Hermite polynomials. 1
1, 6, 38, 252, 1740, 12456, 92136, 702288, 5503632, 44258400, 364615776, 3072862656, 26458723008, 232501041792, 2082933048960, 19007627463936, 176533756252416, 1667446616360448, 16006827410744832, 156069042653445120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

In Maple notation, a(n) = I^n*HermiteH(n, -3*I)

Recurrence: a(n) = 6*a(n-1) + 2*(n-1)*a(n-2). - Vaclav Kotesovec, Oct 13 2012

a(n) ~ 2^(n/2-1/2)*exp(-n/2+3*sqrt(2*n)-9/2)*n^(n/2)*(1+3*sqrt(2)/sqrt(n)). - Vaclav Kotesovec, Oct 13 2012

E.g.f.: exp(x^2+6*x). - Vaclav Kotesovec, Oct 21 2012

MAPLE

seq(expand(I^n*HermiteH(n, -I*3)), n=0..14);

MATHEMATICA

Table[I^n*HermiteH[n, -3I], {n, 0, 20}]

CoefficientList[Series[E^(x^2+6*x), {x, 0, 20}], x]*Range[0, 20]! (* Vaclav Kotesovec, Oct 21 2012 *)

PROG

(PARI) x='x+O('x^66); Vec(serlaplace(exp(x^2+6*x))) \\ Joerg Arndt, May 07 2013

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(6*x + x^2))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 10 2018

CROSSREFS

Cf. A000898.

Sequence in context: A215466 A147957 A098410 * A026940 A082427 A192941

Adjacent sequences:  A079946 A079947 A079948 * A079950 A079951 A079952

KEYWORD

nonn

AUTHOR

Karol A. Penson, Jan 19 2003

EXTENSIONS

Edited and extended by Robert G. Wilson v, Jan 22 2003

STATUS

approved

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Last modified January 17 15:12 EST 2020. Contains 330958 sequences. (Running on oeis4.)