A165343 -id:A165343 - cp's OEIS frontend

A227143 Hankel determinants of order n of A225439(n): a(n)=det[A225439(i+j-2)], i,j=0..n, n>=0.

1, 1, 12, 567, 122472, 126660105, 640190834712, 15987980408180508, 1985745116187976972608, 1231754497376142871049675940, 3826847477714307687323719819461000, 59670909707615018862830973519922857945375

Offset: 0

Karol A. Penson, Jul 02 2013

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..52

Cf. A225439, A101799, A101800, A165343, A165344, A059486.

with(LinearAlgebra):
A225439 := proc(n) add(binomial(k,n-k)*3^(k)*(-1)^(n-k)*binomial(n+k-1,n-1), k=0..n) end:
hank0:= (i, j)-> A225439(i+j-2):
a:= proc(n) Determinant(Matrix(n,n,hank0)) end:
seq(a(n), n=0..10);

A225439[n_] := Sum[Binomial[k, n-k]*3^k*(-1)^(n-k)*Binomial[n+k-1, n-1], {k, 0, n}]; a[n_] := Det[Table[A225439[i+j-2], {i, n}, {j, n}]]; a[0] = 1; Table[ a[n], {n, 0, 11}] (* Jean-François Alcover, Nov 07 2016 *)

a(n) ~ c * (9/4)^(n^2) * n^(31/36) / 3^(n/2), where c = 2^(5/12) * exp(1/36) * Pi^(1/3) / (A^(1/3) * 3^(7/36) * Gamma(1/3)^(2/3)) = 0.774669663248120327054918681212809967565811826042305406436705141... and A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Feb 24 2019

A227379 Hankel determinants of order n of A225439(n): a(n) = det[A225439(i+j-1)], i,j=0..n, n>=0.

Original entry on oeis.org

1, 3, 45, 3402, 1299078, 2507870079, 24487299427734, 1209640056157393380, 302358334494179897593596, 382459771435292361460924379370, 2448391839613471201062299337071282925

Offset: 0

Karol A. Penson, Jul 09 2013

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..53

Cf. A227143, A225439, A101799, A101800, A165343, A165344, A059486.

with(LinearAlgebra):
A225439 := proc(n) add(binomial(k, n-k)*3^(k)*(-1)^(n-k)*binomial(n+k-1, n-1), k=0..n) end:
hank1:= (i, j)-> A225439(i+j-1):
a:= proc(n) Determinant(Matrix(n, n, hank1)) end:
seq(a(n), n=0..10);

A225439[n_] := Sum[Binomial[k, n-k]*3^k*(-1)^(n-k)*Binomial[n+k-1, n-1], {k, 0, n}]; a[n_] := Det[Table[A225439[i+j-1], {i, n}, {j, n}]]; a[0] = 1; Table[ a[n], {n, 0, 11}] (* Vaclav Kotesovec, Feb 24 2019, after Jean-François Alcover *)

a(n) ~ c * 3^(n*(4*n + 3)/2) * n^(1/36) / 4^(n*(n+1)), where c = 3^(11/36) * exp(1/36) * Gamma(1/3)^(1/3) / (2^(7/12) * A^(1/3) * Pi^(1/6)) = 1.0139930857022957587164044116685749094666597031981229532... and A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Feb 24 2019

cp's OEIS Frontend

A227143 Hankel determinants of order n of A225439(n): a(n)=det[A225439(i+j-2)], i,j=0..n, n>=0.

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