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Expansion of e.g.f. 1 / (exp(-x^3/6) - x).
2

%I #13 Aug 23 2024 08:01:05

%S 1,1,2,7,32,180,1210,9520,85680,867160,9749600,120582000,1626994600,

%T 23782158400,374367193200,6314037129400,113591474796800,

%U 2171267969270400,43944509528920000,938808209417478400,21111813400597920000,498498097342637392000

%N Expansion of e.g.f. 1 / (exp(-x^3/6) - x).

%F a(n) = n! * Sum_{k=0..floor(n/3)} ((n-3*k+1)/6)^k/k!.

%p A375395 := proc(n)

%p n!*add(((n-3*k+1)/6)^k/k!,k=0..floor(n/3)) ;

%p end proc:

%p seq(A375395(n),n=0..60) ; # _R. J. Mathar_, Aug 23 2024

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x^3/6)-x)))

%o (PARI) a(n) = n!*sum(k=0, n\3, ((n-3*k+1)/6)^k/k!);

%Y Cf. A072597, A375394.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 21 2024