A385698 E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(-x))*(A(x) + A(w*x) + A(w^2*x))/6 ), where w = exp(2*Pi*i/3).

1, 1, 1, 4, 29, 256, 1501, 28715, 266001, 4590064, 99387041, 2223185152, 30919119661, 1183047504809, 21297988134879, 656259407452756, 23786602263322385, 856920025214144512, 18903506095173283273, 1086514755640058121323, 29116796997476903252841

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{i, j, k>=0 and i+2*j+3*k=n-1} (n-i) * a(i) * a(2*j) * a(3*k)/(i! * (2*j)! * (3*k)!).

Mathematica

terms = 21; w = Exp[2*Pi*I/3]; A[_] = 0; Do[A[x_] = Exp[x*(A[x] + A[-x])*(A[x] + A[w*x] + A[w^2*x])/6 ] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0, terms-1]!//Simplify (* Stefano Spezia, Jul 07 2025 *)

Crossrefs

Cf. A385699.

Sequence in context: A387037 A208812 A291103 * A125808 A379875 A367752

Adjacent sequences: A385695 A385696 A385697 * A385699 A385700 A385701

Keyword

nonn

Author

Seiichi Manyama, Jul 07 2025

Status

approved