1,2

P. Blasiak, K. A. Penson and A. I. Solomon, The Boson Normal Ordering Problem and Generalized Bell Numbers

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem.

P. Blasiak, A. Horzela, K. A. Penson, G.H.E. Duchamp and A. I. Solomon, Boson normal ordering via substitutions and Sheffer-type polynomials

E.g.f. exp(-1+1/sqrt(1-2*x))-1.

Representation of a(n) as n-th moment of a positive function on (0, infinity): a(n)=int(x^n* (x/2)^(-1/2)*exp(-x/2)*(2*hypergeom([], [3/2, 1/2], 1/8*x)/Pi^(1/2)+1/2*sqrt(2)*sqrt(x)*hypergeom([], [2, 3/2], 1/8*x))/(4*exp(1)), x=0..infinity), n=1, 2... - Karol A. Penson (penson(AT)lptl.jussieu.fr), Jun 27, 2002

Asymptotic expansion for large n: a(n) -> 2^(1/6)*(n^(-1/3) + 2^(-7/3)*n^(-2/3) + O(1/n))*(2*n)^n*exp(-n+(3/2)*(2*n)^(1/3))/(sqrt(3)*exp(1)); (the nature of this approximation of a(n) is the same as that of Stirling approximation of n! ). - Karol A. Penson (penson(AT)lptl.jussieu.fr), Sep 02, 2002

Cf. A000262.

Sequence in context: A105628 A064299 A038174 this_sequence A047733 A007830 A060911

Adjacent sequences: A049115 A049116 A049117 this_sequence A049119 A049120 A049121

easy,nonn

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)