A308849 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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}]