1,2

Generalized Bell numbers B(5,1;n).

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.

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.

E.g.f. exp(-1+1/(1-4*x)^(1/4))-1.

Representation of a(n) as the n-th moment of a positive function on positive half-axis (Stieltjes moment problem), in Maple notation: a(n)=int(x^n*exp(-1)*exp(-1/4*x)*(1/96*x*hypergeom([],[5/4, 3/2, 7/4, 2],1/1024*x)+ 1/8*4^(3/4)*x^(1/4)/Pi*2^(1/2)*GAMMA(3/4)*hypergeom([],[1/4, 1/2,3/4, 5/4],1/1024*x)+1/8*4^(1/2)*x^(1/2)/Pi^(1/2)*hypergeom([],[1/2, 3/4, 5/4,3/2],1/1024*x)+1/24*4^(1/4)*x^(3/4)/GAMMA(3/4)*hypergeom([],[3/4, 5/4, 3/2,7/4],1/1024*x))/x, x=0..infinity),n=1,2... . - Karol A. Penson (penson(AT)lptl.jussieu.fr), Dec 16 2007

Cf. A049119, generalized Bell numbers B(4, 1, n).

Sequence in context: A064088 A047737 A086403 this_sequence A056546 A127695 A144343

Adjacent sequences: A049117 A049118 A049119 this_sequence A049121 A049122 A049123

easy,nonn

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