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A278903
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Second series of Hankel determinants based on Bell numbers of argument k^2, Bell(k^2).
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1
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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MAPLE
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with(LinearAlgebra), with(combinat):
h21:=(i, j)->bell((i+j-1)^2):
seq(Determinant(Matrix(kk, kk, h21)), kk=0..6);
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MATHEMATICA
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Table[Det[Table[BellB[(i + j - 1)^2], {i, n}, {j, n}]], {n, 5}], n=>1.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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