A308849 Expansion of e.g.f. 1 / (BesselI(0,2*x) + BesselI(1,2*x)).

1, -1, 0, 3, -6, -10, 100, -175, -1470, 11214, -4032, -447678, 2813580, 8767044, -254393568, 1156311585, 14213048850, -237139066450, 423094740640, 26925567437054, -323136231452892, -998293111680228, 67449022208054760, -562713810943757746, -7585754355598687268, 220643947556639812100

Offset

0,4

Comments

E.g.f. is inverse of e.g.f. for A001405.

Links

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

Formula

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

Mathematica

nmax = 25; CoefficientList[Series[1/(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[k, Floor[k/2]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 25}]

Crossrefs

Cf. A001405, A308850.

Sequence in context: A351131 A061380 A350993 * A354000 A368173 A125567

Adjacent sequences: A308846 A308847 A308848 * A308850 A308851 A308852

Keyword

sign

Author

Ilya Gutkovskiy, Jun 28 2019

Status

approved