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

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

Offset

0,2

Links

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

Formula

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

Maple

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);

Mathematica

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 *)

Crossrefs

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

Sequence in context: A228903 A198952 A099168 * A004105 A060336 A268196

Adjacent sequences: A227376 A227377 A227378 * A227380 A227381 A227382

Keyword

nonn

Author

Karol A. Penson, Jul 09 2013

Status

approved