OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..257
FORMULA
Sum_{n>=0} a(n) * x^n / (n!)^2 = log(1 + x * BesselI(0,2*sqrt(x))).
Sum_{n>=0} a(n) * x^n / (n!)^2 = log(1 + Sum_{n>=1} n^2 * x^n / (n!)^2).
MAPLE
S:= series(log(1+x*BesselI(0, 2*sqrt(x))), x, 31):
0, seq(coeff(S, x, n)*(n!)^2, n=1..30); # Robert Israel, Jan 07 2024
MATHEMATICA
a[0] = 0; a[n_] := a[n] = n^2 - (1/n) * Sum[(Binomial[n, k] (n - k))^2 k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Log[1 + x BesselI[0, 2 Sqrt[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Sep 24 2020
STATUS
approved