A375656 Expansion of e.g.f. exp(x^3 + x * exp(x^3/6)).
1, 1, 1, 7, 29, 81, 541, 3781, 18537, 129529, 1171961, 8446131, 66198661, 683784817, 6492131829, 59303102041, 664191218321, 7659196889841, 82391350746097, 991483941558079, 13066764825298221, 164001743446274161, 2139651772557011021, 30946063565684912877
Offset: 0
Keywords
Programs
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Mathematica
With[{nn=30},CoefficientList[Series[Exp[x^3+x Exp[x^3/6]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 12 2025 *) -
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^3+x*exp(x^3/6)))) -
PARI
a(n) = n!*sum(k=0, n\3, ((n-3*k+6)/6)^k/(k!*(n-3*k)!));
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} ((n-3*k+6)/6)^k / (k! * (n-3*k)!).