A376516 - OEIS

A376516

E.g.f. satisfies A(x) = exp(x^3 * A(x) / (1 - x)).

1, 0, 0, 6, 24, 120, 1800, 20160, 221760, 3507840, 59875200, 1037836800, 20776694400, 459761702400, 10686605529600, 268901439206400, 7318617546240000, 210804082384896000, 6440850193262284800, 209115023566972723200, 7157303732396353536000, 257535328655939862528000

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..21.

Eric Weisstein's World of Mathematics, Lambert W-Function.

FORMULA

E.g.f.: exp( -LambertW(-x^3 / (1-x)) ).

a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) * binomial(n-2*k-1,n-3*k)/k!.

PROG

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

(PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*binomial(n-2*k-1, n-3*k)/k!);