The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #11 May 27 2022 02:38:22
%S 0,1,5,12,21,33,47,64,83,105,129,155,184,216,250,286,325,366,410,456,
%T 505,556,610,666,725,786,849,915,984,1055,1128,1204,1282,1363,1446,
%U 1532,1620,1711,1804,1900,1998,2098,2201,2307,2415,2525,2638,2753,2871,2991,3114,3239,3367,3497,3630,3765,3903,4043,4185,4330,4477,4627,4780,4935
%N List of k such that sign(A009273(k)) = sign(A009273(k+1)).
%C Conjecture: Lim_{n->infinity) a(n)/n^2 = Pi^2/8 = A111003 = 1.2337...
%e 12 is in the sequence because A009273(12) = -454930757753597952 and A009273(13) = -94991612229069430784 have the same sign.
%t nmax = 400; A009273 = Table[(CoefficientList[Series[E^(x*Tanh[x]), {x, 0, 2*nmax}], x]*Range[0, 2*nmax]!)[[k]], {k, 1, 2*nmax, 2}]; Join[{0}, Select[Range[nmax-1], A009273[[#]]*A009273[[#-1]] > 0 &] - 1]
%Y Cf. A009273, A354246, A354425.
%K nonn
%O 1,3
%A _Vaclav Kotesovec_, May 25 2022