A345244 G.f. A(x) satisfies: A(x) = x + x^2 * exp(3 * Sum_{k>=1} (-1)^(k+1) * A(x^k) / k).

1, 1, 3, 6, 19, 57, 177, 586, 1950, 6642, 22990, 80400, 284346, 1014237, 3644841, 13185810, 47976382, 175458798, 644630064, 2378084209, 8805524949, 32714828733, 121917589291, 455625246297, 1707142362234, 6411576477380, 24133229559243, 91023263056629, 343964618949140, 1302098673500514

Offset

1,3

Links

Table of n, a(n) for n=1..30.

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} (-1)^(k/d+1) * d * a(d) ) * a(n-k+2).

Mathematica

nmax = 30; A[_] = 0; Do[A[x_] = x + x^2 Exp[3 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] = a[2] = 1; a[n_] := a[n] = (3/(n - 2)) Sum[Sum[(-1)^(k/d + 1) d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 30}]

Crossrefs

Cf. A007560, A052757, A345243, A345245.

Sequence in context: A320174 A248603 A332344 * A052393 A024607 A186022

Adjacent sequences: A345241 A345242 A345243 * A345245 A345246 A345247

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 11 2021

Status

approved