%I #7 Jun 28 2019 21:18:03
%S 1,-3,8,-17,18,58,-364,369,6194,-37382,-28848,1717274,-8592644,
%T -47472804,918146560,-2911313551,-61122074382,806675821162,
%U 46813084592,-105331573943466,1018198168087636,6417696715221572,-247555432672498872,1535509971584425358,34028097257000628028,-764203552200012087252
%N Expansion of e.g.f. exp(-2*x) / (BesselI(0,2*x) + BesselI(1,2*x)).
%C E.g.f. is inverse of e.g.f. for A001700.
%F E.g.f.: 1 / Sum_{k>=0} binomial(2*k+1,k+1)*x^k/k!.
%t nmax = 25; CoefficientList[Series[Exp[-2 x]/(BesselI[0, 2 x] + BesselI[1, 2 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] Binomial[2 k + 1, k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 25}]
%Y Cf. A001700, A178955, A246432, A308847, A308849.
%K sign
%O 0,2
%A _Ilya Gutkovskiy_, Jun 28 2019