cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A278868 Second series of Hankel determinants based on hyperfactorial/4.

Original entry on oeis.org

1, 1, 6183, 5772211367657472, 76148812142946816440318638031477145600000, 3940613226283843476344831941863494501303228636304800836707599745608602091520000000000
Offset: 0

Views

Author

Karol A. Penson, Nov 29 2016

Keywords

Comments

It would be useful to know the formula for this sequence.

Crossrefs

Programs

  • Maple
    a:= n-> LinearAlgebra[Determinant](Matrix(n, (i, j)->
            (t-> mul(k^k, k=0..t)/4)(i+j))):
    seq(a(n), n=0..6);  # Alois P. Heinz, Nov 29 2016
  • Mathematica
    Table[Det[Table[Hyperfactorial[i + j]/4, {i, n}, {j, n}]], {n, 6}]

A278897 First series of Hankel determinants based on Bell numbers of argument k^2, Bell(k^2).

Original entry on oeis.org

1, 1, 14, 146275425484, 558429168112511379835233509679413804180016
Offset: 0

Views

Author

Karol A. Penson, Nov 30 2016

Keywords

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.

Crossrefs

Programs

  • 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.

A278903 Second series of Hankel determinants based on Bell numbers of argument k^2, Bell(k^2).

Original entry on oeis.org

1, 1, 20922, 96938760190744854628604, 1039473181175725249030299777705981025900981837012416973957739853576960
Offset: 0

Views

Author

Karol A. Penson, Nov 30 2016

Keywords

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.

Crossrefs

Programs

  • 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.
Showing 1-3 of 3 results.