A358265 Expansion of e.g.f. 1/(1 - x * exp(x^3/6)).

1, 1, 2, 6, 28, 160, 1080, 8470, 76160, 771120, 8671600, 107245600, 1446984000, 21150929800, 332950217600, 5615507898000, 101024594070400, 1931055071545600, 39082823446867200, 834945681049480000, 18776164188349568000, 443348081412556320000

Offset: 0

Author

Seiichi Manyama, Nov 06 2022

Keywords

• nonn
• easy

Crossrefs

Cf. A006153, A358264.

Cf. A354551, A358065.

Programs

Maple

g := 1/(1-x*exp(x^3/6)) ;
taylor(%,x=0,70) ;
L := gfun[seriestolist](%) ;
seq( op(i,L)*(i-1)!,i=1..nops(L)) ; # R. J. Mathar, Mar 13 2023

PARI

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

PARI

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

Formula

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

a(n) ~ n! / ((1 + LambertW(1/2)) * (2*LambertW(1/2))^(n/3)). - Vaclav Kotesovec, Nov 13 2022