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A089148 E.g.f.: 1/(exp(x) - x). 7
1, 0, -1, -1, 5, 19, -41, -519, -183, 19223, 73451, -847067, -8554547, 32488611, 977198559, 1325135969, -116987762287, -860498433233, 13730866757587, 243612350234973, -1120827248102379, -62079344419449925, -185852602587850681, 15185914155303053209 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

INVERTi transform of [1, 1, 1/2, 1/6, 1/24, 1/120,...] = [1, 0, -1/2, 1/6, 5/24, -19/120, -41/720, 519/5040, -183/40320, -19223/362880,...]. - Gary W. Adamson, Oct 08 2008

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

E.g.f.: -(1+1/(G(0)-1))/x where G(k) = 1 - (k+1)/(1 - x/(x + (k+1)^2/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Dec 07 2012

a(n) = sum(k=0..n, sum(l=0,k, k!*C(n,l)*(-1)^(k-l)*stirling2(n-l,k-l))). - Vladimir Kruchinin, May 29 2013

Lim sup n->infinity |a(n)/n!|^(1/n) = 1/abs(LambertW(-1)) = 0.727507111152... - Vaclav Kotesovec, Aug 13 2013

MAPLE

b:= proc(n) b(n):= -`if` (n<0, 1, add(b(n-i)/(i-1)!, i=1..n+1)) end:

a:= n-> (-1)^n*n!*b(n):

seq(a(n), n=0..30);  # Alois P. Heinz, May 29 2013

MATHEMATICA

a = CoefficientList[Series[1/( E^ x - x), {x, 0, 30}], x]; Table[(n - 1)! *a[[n]], {n, 1, Length[a]}] (* Roger L. Bagula and Gary W. Adamson, Oct 06 2008 *)

With[{nn=30}, CoefficientList[Series[1/(Exp[x]-x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 03 2017 *)

PROG

(Maxima) a(n):=sum(sum(k!*binomial(n, l)*(-1)^(k-l)*stirling2(n-l, k-l), l, 0, k), k, 0, n); /* Vladimir Kruchinin, May 29 2013 */

(PARI) x='x+O('x^66); Vec(serlaplace(1/(exp(x)-x))) \\ Joerg Arndt, May 29 2013

(Sage)

def A089148_list(len):

    f, R, C = 1, [], [1]+[0]*len

    for n in (1..len):

        for k in range(n, 0, -1):

            C[k] = C[k-1]*(1/(k-1) if k>1 else 1)

        C[0] = -sum((-1)^k*C[k] for k in (1..n))

        R.append(C[0]*f)

        f *= n

    return R

print A089148_list(24) # Peter Luschny, Feb 21 2016

CROSSREFS

Cf. A006153.

Sequence in context: A091568 A147307 A234801 * A098319 A022267 A094465

Adjacent sequences:  A089145 A089146 A089147 * A089149 A089150 A089151

KEYWORD

sign

AUTHOR

Wouter Meeussen, Dec 06 2003

STATUS

approved

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Last modified October 21 12:12 EDT 2019. Contains 328299 sequences. (Running on oeis4.)