OFFSET
1,5
FORMULA
G.f.: x + x^2 / Product_{n>=1} (1 - (-x)^n)^((-1)^n*a(n)).
a(n+2) = (1/n) * Sum_{k=1..n} (-1)^k * ( Sum_{d|k} (-1)^d * d * a(d) ) * a(n-k+2).
a(n) ~ c * d^n / n^(3/2), where d = 2.04187801797233390910633071122033289228232310618876458... and c = 0.624667034123125135463988884805660643637934291759335... - Vaclav Kotesovec, Jun 19 2021
MATHEMATICA
nmax = 40; A[_] = 0; Do[A[x_] = x + x^2 Exp[Sum[A[(-1)^(k + 1) x^k]/k, {k, 1, nmax}]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
a[1] = a[2] = 1; a[n_] := a[n] = (1/(n - 2)) Sum[(-1)^k Sum[(-1)^d d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 40}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 11 2021
STATUS
approved