A346032 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, 0, 2, 1, 1, 4, 2, 4, 9, 4, 14, 20, 15, 43, 48, 55, 127, 127, 199, 363, 379, 684, 1048, 1229, 2263, 3100, 4163, 7288, 9558, 14231, 23222, 30673, 48404, 74113, 101631, 163048, 239282, 343196, 545318, 785139, 1169148, 1818866, 2619072, 3991888, 6079434

Offset

1,8

Links

Table of n, a(n) for n=1..50.

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} (-1)^(k/d+1) * d * a(d) ) * a(n-k).

Maple

a:= proc(n) option remember; `if`(n<4, signum(n-1), add(a(n-k)*add(
     (-1)^(k/d+1)*d*a(d), d=numtheory[divisors](k)), k=1..n-3)/(n-3))
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, Jul 01 2021

Mathematica

nmax = 50; A[_] = 0; Do[A[x_] = x^2 + x^3 Exp[Sum[(-1)^(k + 1) 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[(-1)^(k/d + 1) d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 3}]; Table[a[n], {n, 1, 50}]

Crossrefs

Cf. A007560, A316075, A346031.

Sequence in context: A177276 A123199 A212282 * A157125 A335941 A157143

Adjacent sequences: A346029 A346030 A346031 * A346033 A346034 A346035

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 01 2021

Status

approved