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A278897
First series of Hankel determinants based on Bell numbers of argument k^2, Bell(k^2).
1
1, 1, 14, 146275425484, 558429168112511379835233509679413804180016
OFFSET
0,3
COMMENTS
If we regard Bell(k^2) as the k-th Stieltjes moment for k>=0, then the solution of the Stieltjes moment problem is given in the P. Blasiak et al. reference, see below. We conjecture that a(n)>0 for n>=0. The positivity of these Hankel determinants a(n), n>=0 is one of the conditions for the existence of a positive solution. Apparently this solution is not unique.
LINKS
P. Blasiak, K. A. Penson and A. I. Solomon, Dobinsky-type relations and the log-normal distribution, J. Phys. A: Math. Gen. 36, L273 (2003), arXiv: quant-ph/0303030, 2003.
MAPLE
with(LinearAlgebra), with(combinat):
h20:=(i, j)->bell((i+j-2)^2):
seq(Determinant(Matrix(kk, kk, h20)), kk=0..6);
MATHEMATICA
Table[Det[Table[BellB[(i + j - 2)^2], {i, n}, {j, n}]], {n, 6}], n=>1.
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Nov 30 2016
STATUS
approved