login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A155456 Write (1+1/x)*log(1+x) = Sum c(n)*x^n; then a(n) = (n+1)!*c(n). 0
-1, -1, 1, -2, 6, -24, 120, -720, 5040, -40320, 362880, -3628800, 39916800, -479001600, 6227020800, -87178291200, 1307674368000, -20922789888000, 355687428096000, -6402373705728000, 121645100408832000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Apart from initial terms and signs, identical to A000142.

a(n-1), n >= 0, is the negative of the alternating row sum of A048994 (Stirling1) with e.g.f. -1/(1+x). -  - Wolfdieter Lang, May 09 2017

LINKS

Table of n, a(n) for n=0..20.

P. W. Anderson, D. J. Thouless, E. Abrahams and D. S. Fisher, New method for a scaling theory of localization, Physical Review B, 1980.

FORMULA

G.f. -1-x+x^2/(G(0)+x) where G(k)= 1 + (k+1)*x/(1 + x*(k+2)/G(k+1)); (continued fraction, 2-step). - Sergei N. Gladkovskii, Aug 14 2012

G.f.: conjecture: T(0)*x^2/(1+2*x) - 1 - x, where T(k) = 1 - x^2*(k+1)*(k+2)/(x^2*(k+1)*(k+2) - (1+2*x*(k+1))*(1+2*x*(k+2))/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 19 2013

MATHEMATICA

p[x] = -(1 + 1/x)*Log[1 + x];

Table[ (n + 1)!*SeriesCoefficient[ Series[p[x], {x, 0, 30}], n], {n, 0, 30}]

CROSSREFS

Cf. A048994.

Sequence in context: A154659 A254523 A289282 * A124355 A133942 A159333

Adjacent sequences:  A155453 A155454 A155455 * A155457 A155458 A155459

KEYWORD

sign,easy

AUTHOR

Roger L. Bagula, Jan 22 2009

EXTENSIONS

Edited by N. J. A. Sloane, Jun 02 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 16 20:51 EDT 2021. Contains 347473 sequences. (Running on oeis4.)