OFFSET
0,4
FORMULA
Sum_{n>=0} a(n) * x^n / (n!)^2 = log(1 + sqrt(x) * BesselI(1,2*sqrt(x))).
Sum_{n>=0} a(n) * x^n / (n!)^2 = log(1 + Sum_{n>=1} n * x^n / (n!)^2).
MATHEMATICA
a[0] = 0; a[n_] := a[n] = n - (1/n) Sum[Binomial[n, k]^2 (n - k) k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[Log[1 + Sqrt[x] BesselI[1, 2 Sqrt[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Sep 02 2020
STATUS
approved