|
%I #13 Apr 08 2023 15:10:15
%S 0,2,6,10,16,22,29,37,45,54,63,73,83,93,104,116,128,140,153,166,179,
%T 193,207,221,236,251,266,282,298,314,331,347,364,382,399,417,435,454,
%U 473,491,511,530,550,570,590,610,631,652,673,694,715,737,759,781,804,826,849,872,895,919,942,966,990
%N List of k such that sign(A009277(k)) = sign(A009277(k+1)).
%C What is the limit of a(n) / n^(3/2) ?
%H Vaclav Kotesovec, <a href="/A354425/b354425.txt">Table of n, a(n) for n = 1..182</a>
%e 2 is in the sequence because A009277(2) = -4 and A009277(3) = -88 have the same sign.
%e 6 is in the sequence because A009277(6) = 675776 and A009277(7) = 903834752 have the same sign.
%t nmax = 500; A009277 = Table[(CoefficientList[Series[Exp[Tanh[x]^2], {x, 0, 2*nmax}], x] * Range[0, 2*nmax]!)[[k]], {k, 3, 2*nmax, 2}]; Join[{0}, Select[Range[nmax-2], A009277[[#]]*A009277[[#+1]] > 0 &]]
%t With[{nn=2000},SequencePosition[Sign[Take[CoefficientList[Series[Exp[Tanh[x]^2],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]],{x_,x_}]][[;;,1]]-1 (* _Harvey P. Dale_, Apr 08 2023 *)
%Y Cf. A009277, A354246, A354399.
%K nonn
%O 1,2
%A _Vaclav Kotesovec_, May 27 2022, following a suggestion from _Paul D. Hanna_
|
