A123512 Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively.

1, 10, 105, 1190, 14630, 194796, 2798670, 43204260, 713655855, 12564061510, 234896893231, 4648313235930, 97068707038940, 2133251854548920, 49215687006553740, 1189262114277026856, 30037396074996304365

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..439

Formula

E.g.f.: (1/(1-x)^5)*exp(x/(1-x))*LaguerreL(4,-x/(1-x)).

From Vaclav Kotesovec, Nov 13 2017: (Start)

Recurrence: n*a(n) = 2*n*(n+4)*a(n-1) - (n-1)*(n+3)*(n+4)*a(n-2).

a(n) ~ exp(2*sqrt(n)-n-1/2) * n^(n + 17/4) / (3*2^(7/2)) * (1 + 31/(48*sqrt(n))).

(End)

Mathematica

CoefficientList[ Series[(1/(1 - x)^5)*Exp[x/(1 - x)]LaguerreL[4, -x/(1 - x)], {x, 0, 16}], x]*Range[0, 16]! (* Robert G. Wilson v, Oct 03 2006 *)

Prog

(PARI)
LaguerreL(n, v='x) = {
  my(x='x+O('x^(n+1)), t='t);
  subst(polcoeff(exp(-x*t/(1-x))/(1-x), n), 't, v);
};
N=17; x='x+O('x^N); Vec(serlaplace((1/(1-x)^5)*exp(x/(1-x))*LaguerreL(4, -x/(1-x)))) \\ Gheorghe Coserea, Oct 26 2017

Crossrefs

Cf.: A002720, A052852, A123510, A123511.

Sequence in context: A233830 A046715 A145713 * A079515 A024131 A000457

Adjacent sequences: A123509 A123510 A123511 * A123513 A123514 A123515

Keyword

nonn

Author

Karol A. Penson, Oct 02 2006

Extensions

a(0)=1 prepended by Gheorghe Coserea, Oct 26 2017

Status

approved