A358265 - OEIS

%I #14 Mar 13 2023 16:04:03

%S 1,1,2,6,28,160,1080,8470,76160,771120,8671600,107245600,1446984000,

%T 21150929800,332950217600,5615507898000,101024594070400,

%U 1931055071545600,39082823446867200,834945681049480000,18776164188349568000,443348081412556320000

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

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

%F a(n) ~ n! / ((1 + LambertW(1/2)) * (2*LambertW(1/2))^(n/3)). - _Vaclav Kotesovec_, Nov 13 2022

%p g := 1/(1-x*exp(x^3/6)) ;

%p taylor(%,x=0,70) ;

%p L := gfun[seriestolist](%) ;

%p seq( op(i,L)*(i-1)!,i=1..nops(L)) ; # _R. J. Mathar_, Mar 13 2023

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

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

%Y Cf. A006153, A358264.

%Y Cf. A354551, A358065.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Nov 06 2022