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A278903 Second series of Hankel determinants based on Bell numbers of argument k^2, Bell(k^2). 1
1, 1, 20922, 96938760190744854628604, 1039473181175725249030299777705981025900981837012416973957739853576960 (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):

h21:=(i, j)->bell((i+j-1)^2):

seq(Determinant(Matrix(kk, kk, h21)), kk=0..6);

MATHEMATICA

Table[Det[Table[BellB[(i + j - 1)^2], {i, n}, {j, n}]], {n, 5

  }], n=>1.

CROSSREFS

Cf. A000110, A277829, A278770, A278868, A278860, A278897.

Sequence in context: A031813 A043654 A188104 * A233649 A262668 A344354

Adjacent sequences:  A278900 A278901 A278902 * A278904 A278905 A278906

KEYWORD

nonn

AUTHOR

Karol A. Penson, Nov 30 2016

STATUS

approved

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Last modified October 15 17:30 EDT 2021. Contains 348033 sequences. (Running on oeis4.)