A346030 G.f. A(x) satisfies: A(x) = x^2 + x^3 * exp(A(x) + A(x^2)/2 + A(x^3)/3 + A(x^4)/4 + ...).

0, 1, 1, 0, 1, 1, 1, 2, 3, 3, 6, 8, 11, 18, 26, 37, 60, 87, 132, 206, 310, 475, 742, 1130, 1759, 2737, 4236, 6618, 10348, 16139, 25350, 39767, 62456, 98401, 155047, 244570, 386639, 611298, 967874, 1534297, 2433584, 3864154, 6141560, 9766908, 15547187, 24766037, 39476846

Offset

1,8

Links

Table of n, a(n) for n=1..47.

Formula

G.f.: x^2 + x^3 / Product_{n>=1} (1 - x^n)^a(n).

a(1) = 0, a(2) = 1, a(3) = 1; a(n) = (1/(n - 3)) * Sum_{k=1..n-3} ( Sum_{d|k} d * a(d) ) * a(n-k).

a(n) ~ c * d^n / n^(3/2), where d = 1.646504994482771446591056040381099740295861136174688956979834656... and c = 0.8402317368556115946120005582458627329843217960728964299829... - Vaclav Kotesovec, Jul 06 2021

Maple

a:= proc(n) option remember; `if`(n<4, signum(n-1), add(a(n-k)*
       add(d*a(d), d=numtheory[divisors](k)), k=1..n-3)/(n-3))
    end:
seq(a(n), n=1..47);  # Alois P. Heinz, Jul 01 2021

Mathematica

nmax = 47; A[_] = 0; Do[A[x_] = x^2 + x^3 Exp[Sum[A[x^k]/k, {k, 1, nmax}]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
a[1] = 0; a[2] = 1; a[3] = 1; a[n_] := a[n] = (1/(n - 3)) Sum[Sum[d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 3}]; Table[a[n], {n, 1, 47}]

Crossrefs

Cf. A007562, A218020, A346020.

Sequence in context: A158278 A187505 A027100 * A261090 A183560 A060840

Adjacent sequences: A346027 A346028 A346029 * A346031 A346032 A346033

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 01 2021

Status

approved