%I #24 Feb 24 2019 15:17:11
%S 1,1,12,567,122472,126660105,640190834712,15987980408180508,
%T 1985745116187976972608,1231754497376142871049675940,
%U 3826847477714307687323719819461000,59670909707615018862830973519922857945375
%N Hankel determinants of order n of A225439(n): a(n)=det[A225439(i+j-2)], i,j=0..n, n>=0.
%H Vaclav Kotesovec, <a href="/A227143/b227143.txt">Table of n, a(n) for n = 0..52</a>
%F 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
%p with(LinearAlgebra):
%p A225439 := proc(n) add(binomial(k,n-k)*3^(k)*(-1)^(n-k)*binomial(n+k-1,n-1), k=0..n) end:
%p hank0:= (i, j)-> A225439(i+j-2):
%p a:= proc(n) Determinant(Matrix(n,n,hank0)) end:
%p seq(a(n), n=0..10);
%t 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 *)
%Y Cf. A225439, A101799, A101800, A165343, A165344, A059486.
%K nonn
%O 0,3
%A _Karol A. Penson_, Jul 02 2013
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