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A292866 a(n) = n! * [x^n] exp(n*(1 - exp(x))). 9
1, -1, 2, -3, -20, 370, -4074, 34293, -138312, -2932533, 106271090, -2192834490, 32208497124, -206343936097, -7657279887698, 412496622532785, -12455477719752976, 260294034150380430, -2256541295745391542, -122593550603339550843, 8728842979656718306780 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..415

FORMULA

a(n) = exp(n) * Sum_{k>=0} (-n)^k*k^n/k!. - Ilya Gutkovskiy, Jul 13 2019

a(n) = Sum_{k=0..n} (-n)^k * Stirling2(n,k). - Seiichi Manyama, Jul 28 2019

MAPLE

b:= proc(n, k) option remember; `if`(n=0, 1,

      -(1+add(binomial(n-1, j-1)*b(n-j, k), j=1..n-1))*k)

    end:

a:= n-> b(n$2):

seq(a(n), n=0..30);  # Alois P. Heinz, Sep 25 2017

MATHEMATICA

Table[n!*SeriesCoefficient[E^(n*(1 - E^x)), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 25 2017 *)

PROG

(Ruby)

def ncr(n, r)

  return 1 if r == 0

  (n - r + 1..n).inject(:*) / (1..r).inject(:*)

end

def A(k, n)

  ary = [1]

  (1..n).each{|i| ary << k * (0..i - 1).inject(0){|s, j| s + ncr(i - 1, j) * ary[j]}}

  ary

end

def A292866(n)

  (0..n).map{|i| A(-i, i)[-1]}

end

p A292866(20)

(PARI) {a(n) = sum(k=0, n, (-n)^k*stirling(n, k, 2))} \\ Seiichi Manyama, Jul 28 2019

CROSSREFS

Main diagonal of A292861.

Cf. A242817.

Sequence in context: A177946 A006246 A110372 * A132421 A132500 A129411

Adjacent sequences:  A292863 A292864 A292865 * A292867 A292868 A292869

KEYWORD

sign

AUTHOR

Seiichi Manyama, Sep 25 2017

STATUS

approved

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Last modified June 24 04:02 EDT 2021. Contains 345416 sequences. (Running on oeis4.)