OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..200
P. Blasiak, Karol A. Penson and A. I. Solomon, The general boson normal ordering problem, arXiv:quant-ph/0402027, 2004.
P. Blasiak, Karol A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.
M. Schork, On the combinatorics of normal ordering bosonic operators and deforming it, J. Phys. A 36 (2003) 4651-4665.
FORMULA
In Maple notation, a(n) = (1/12)*n!*(n+1)!*(n+2)!*hypergeom([n+1, n+2, n+3], [2, 3, 4], 1)/exp(1).
MATHEMATICA
ff[n_, k_] = Pochhammer[n - k + 1, k]; a[1, 3] = 1; a[n_, k_] := a[n, k] = Sum[Binomial[3, p]*ff[(n - 1 - p + k), 3 - p]*a[n - 1, k - p], {p, 0, 3} ]; a[n_ /; n < 2, _] = 0; Table[Sum[a[n, k] , {k, 3, 3 n}], {n, 1, 9}] (* Jean-François Alcover, Sep 01 2011 *)
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Karol A. Penson, May 02 2002
EXTENSIONS
Edited by Wolfdieter Lang, Dec 23 2003
STATUS
approved