A079949 Special values of Hermite polynomials.

1, 6, 38, 252, 1740, 12456, 92136, 702288, 5503632, 44258400, 364615776, 3072862656, 26458723008, 232501041792, 2082933048960, 19007627463936, 176533756252416, 1667446616360448, 16006827410744832, 156069042653445120

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