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A317365 Expansion of e.g.f. x*exp(x/(1 + x))/(1 + x). 0
0, 1, 0, -3, 16, -75, 336, -1295, 1632, 55881, -1124000, 16722981, -229985040, 3089923837, -41225160144, 545880027225, -7069180940864, 86130735547665, -882387869940288, 3847692639294541, 171852333163131600, -8392137456287472699, 276055495385982856720, -8067943451470397940543 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Inverse Lah transform of the nonnegative integers (A001477).

LINKS

Table of n, a(n) for n=0..23.

N. J. A. Sloane, Transforms

FORMULA

a(n) = Sum_{k=1..n} binomial(n-1,k-1)*n!/(k-1)!.

MAPLE

a:= proc(n) option remember; add((-1)^(n-k)*

      n!/(k-1)!*binomial(n-1, k-1), k=1..n)

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Jul 26 2018

MATHEMATICA

nmax = 23; CoefficientList[Series[x Exp[x/(1 + x)]/(1 + x) , {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[(-1)^(n - k) Binomial[n - 1, k - 1] n!/(k - 1)!, {k, n}], {n, 0, 23}]

Join[{0}, Table[(-1)^(n + 1) n! LaguerreL[n - 1, 1], {n, 23}]]

CROSSREFS

Cf. A001477, A009940, A052852.

Sequence in context: A038602 A221829 A004303 * A207836 A005947 A005386

Adjacent sequences:  A317362 A317363 A317364 * A317366 A317367 A317368

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jul 26 2018

STATUS

approved

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Last modified February 23 12:03 EST 2019. Contains 320431 sequences. (Running on oeis4.)