A308850 Expansion of e.g.f. exp(-2*x) / (BesselI(0,2*x) + BesselI(1,2*x)).

1, -3, 8, -17, 18, 58, -364, 369, 6194, -37382, -28848, 1717274, -8592644, -47472804, 918146560, -2911313551, -61122074382, 806675821162, 46813084592, -105331573943466, 1018198168087636, 6417696715221572, -247555432672498872, 1535509971584425358, 34028097257000628028, -764203552200012087252

Offset

0,2

Comments

E.g.f. is inverse of e.g.f. for A001700.

Links

Table of n, a(n) for n=0..25.

Formula

E.g.f.: 1 / Sum_{k>=0} binomial(2*k+1,k+1)*x^k/k!.

Mathematica

nmax = 25; CoefficientList[Series[Exp[-2 x]/(BesselI[0, 2 x] + BesselI[1, 2 x]), {x, 0, nmax}], x] Range[0, nmax]!
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}]

Crossrefs

Cf. A001700, A178955, A246432, A308847, A308849.

Sequence in context: A048952 A079666 A193684 * A368273 A335047 A048230

Adjacent sequences: A308847 A308848 A308849 * A308851 A308852 A308853

Keyword

sign

Author

Ilya Gutkovskiy, Jun 28 2019

Status

approved