A385691 E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(w*x) + A(w^2*x))/3 ), where w = exp(2*Pi*i/3).

1, 1, 1, 1, 5, 21, 61, 568, 4257, 20917, 286451, 3099141, 21555865, 390273898, 5524889553, 49790422501, 1121734897937, 19631020478229, 217441607213557, 5862333450708460, 122222268766006641, 1606671304363320805, 50443794604147639487, 1220712011020970521461

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} (3*k+1) * binomial(n-1,3*k) * a(3*k) * a(n-1-3*k).

Mathematica

terms = 24;  w = Exp[2*Pi*I/3]; A[_] = 1; Do[A[x_] = Exp[x*(A[x] + A[w*x] + A[w^2*x])/3] + O[x]^terms // Normal, terms]; Simplify[CoefficientList[A[x], x]Range[0, terms-1]!] (* Stefano Spezia, Jul 07 2025 *)

Crossrefs

Cf. A058014, A124753.

Sequence in context: A356328 A147216 A362573 * A196631 A357723 A342379

Adjacent sequences: A385688 A385689 A385690 * A385692 A385693 A385694

Keyword

nonn

Author

Seiichi Manyama, Jul 07 2025

Status

approved