A345241 G.f. A(x) satisfies: A(x) = x + x^2 * exp(3 * Sum_{k>=1} A(x^k) / k).

1, 1, 3, 9, 28, 93, 315, 1109, 3969, 14505, 53726, 201588, 764001, 2921730, 11257881, 43669590, 170383933, 668236581, 2632898016, 10416893159, 41368099791, 164841324837, 658883345595, 2641064296638, 10613953319448, 42757746556377, 172628891937513, 698398635475974

Offset

1,3

Links

Table of n, a(n) for n=1..28.

Formula

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

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

Mathematica

nmax = 28; A[_] = 0; Do[A[x_] = x + x^2 Exp[3 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] = (3/(n - 2)) Sum[Sum[d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 28}]

Crossrefs

Cf. A006964, A007562, A345200, A345242.

Sequence in context: A368288 A131203 A191637 * A238978 A081914 A361763

Adjacent sequences: A345238 A345239 A345240 * A345242 A345243 A345244

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 11 2021

Status

approved