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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..4.

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.

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

Cf. A000110, A277829, A278770, A278868, A278860.

Sequence in context: A195898 A263500 A164526 * A123652 A127622 A290483

Adjacent sequences:  A278894 A278895 A278896 * A278898 A278899 A278900

KEYWORD

nonn

AUTHOR

Karol A. Penson, Nov 30 2016

STATUS

approved

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Last modified October 26 06:11 EDT 2020. Contains 338027 sequences. (Running on oeis4.)