A375656 - OEIS

%I #9 Aug 23 2024 02:13:25

%S 1,1,1,7,29,81,541,3781,18537,129529,1171961,8446131,66198661,

%T 683784817,6492131829,59303102041,664191218321,7659196889841,

%U 82391350746097,991483941558079,13066764825298221,164001743446274161,2139651772557011021,30946063565684912877

%N Expansion of e.g.f. exp(x^3 + x * exp(x^3/6)).

%F a(n) = n! * Sum_{k=0..floor(n/3)} ((n-3*k+6)/6)^k / (k! * (n-3*k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^3+x*exp(x^3/6))))

%o (PARI) a(n) = n!*sum(k=0, n\3, ((n-3*k+6)/6)^k/(k!*(n-3*k)!));

%Y Cf. A080108, A375655.

%Y Cf. A375634.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Aug 22 2024