OFFSET
1,3
FORMULA
G.f.: x + x^2 / Product_{n>=1} (1 - x^n)^(2*a(n)).
a(n+2) = (2/n) * Sum_{k=1..n} ( Sum_{d|k} d * a(d) ) * a(n-k+2).
a(n) ~ c * d^n / n^(3/2), where d = 3.3437762102302517833309792925121217026126033230718263962128740290952197... and c = 0.3397354606156870289877990463189432389789387070060129709272911771... - Vaclav Kotesovec, Jun 19 2021
MATHEMATICA
nmax = 30; A[_] = 0; Do[A[x_] = x + x^2 Exp[2 Sum[A[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] = (2/(n - 2)) Sum[Sum[d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 11 2021
STATUS
approved