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A123510 Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively. 6
1, 6, 42, 340, 3135, 32466, 373156, 4713192, 64877805, 966466270, 15487707246, 265617899196, 4853435351947, 94114052406570, 1930026941433480, 41728495237790416, 948549349736725401, 22613209058160908982, 564104540143144909810, 14694713818659640322340 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..440

FORMULA

E.g.f.: (1/(1-x)^3)*exp(x/(1-x))*LaguerreL(2,-x/(1-x)), where LaguerreL(p,y) are the Laguerre polynomials.

From Vaclav Kotesovec, Nov 13 2017: (Start)

Recurrence: n*a(n) = 2*n*(n+2)*a(n-1) - (n-1)*(n+1)*(n+2)*a(n-2).

a(n) ~ exp(2*sqrt(n) - n - 1/2) * n^(n + 9/4) / 2^(3/2) * (1 + 31/(48*sqrt(n))).

(End)

MATHEMATICA

max = 16; s = (1/(1-x)^3)*Exp[x/(1-x)]*LaguerreL[2, -x/(1-x)] + O[x]^(max+1); CoefficientList[s, x]*Range[0, max]! (* Jean-Fran├žois Alcover, May 23 2016 *)

PROG

(PARI) m=30; v=concat([6, 42], vector(m-2)); for(n=3, m, v[n]=2*(n+2)*v[n-1]-(n^2 - 1)*((n+2)/n)*v[n-2]); concat([1], v) \\ G. C. Greubel, May 16 2018

(MAGMA) I:=[6, 42]; [1] cat [n le 2 select I[n] else 2*(n+2)*Self(n-1) - (n^2 -1)*((n+2)/n)*Self(n-2): n in [1..30]]; // G. C. Greubel, May 16 2018

CROSSREFS

Cf. A002720, A052852, A123511, A123512.

Sequence in context: A262671 A029588 A001725 * A265871 A132804 A232473

Adjacent sequences:  A123507 A123508 A123509 * A123511 A123512 A123513

KEYWORD

nonn

AUTHOR

Karol A. Penson, Oct 02 2006

EXTENSIONS

a(0)=1 prepended by G. C. Greubel, Oct 31 2017

More terms from G. C. Greubel, May 16 2018

STATUS

approved

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Last modified June 19 07:30 EDT 2019. Contains 324218 sequences. (Running on oeis4.)