OFFSET
0,5
FORMULA
a(0) = 1; a(n) = -(1/n) * Sum_{k=0..n-2} binomial(n,k)^2 * (n-k) * a(k).
MAPLE
A337166 := proc(n)
option remember ;
if n = 0 then
1;
else
add(binomial(n, k)^2*(n-k)*procname(k), k=0..n-2) ;
-%/n ;
end if;
simplify(%) ;
end proc:
seq(A337166(n), n=0..40) ; # R. J. Mathar, Aug 19 2022
MATHEMATICA
nmax = 20; CoefficientList[Series[Exp[1 + x - BesselI[0, 2 Sqrt[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2
a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Binomial[n, k]^2 (n - k) a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 20}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jan 28 2021
STATUS
approved