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!)
A090211 Alternating row sums of array A078739 ((2,2)-Stirling2). 3
1, -1, -1, 41, -375, -3001, 177063, -990543, -144800527, 3644593711, 214013895023, -12488200175463, -553322483517383, 61495192102867639, 2469939623420627543, -448608666325921194271, -19104207797417792353951, 4742067751530355028847327 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.

M. Schork, On the combinatorics of normal ordering bosonic operators and deforming it, J. Phys. A 36 (2003) 4651-4665.

LINKS

Table of n, a(n) for n=1..18.

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem.

FORMULA

a(n) := sum( A078739(n, m)*(-1)^m, m=2..2*n), n>=1. a(0) := +1 may be added.

a(n) = sum(((-1)^k)*(fallfac(k, 2)^n)/k!, k=2..infinity)*exp(1), with fallfac(k, 2)=A008279(k, 2)=k*(k-1) and n>=1. This produces also a(0)=1.

E.g.f. if a(0)=1 is added: exp(1)*(sum(((-1)^k)*exp(k*(k-1)*x)/k!, k=2..infinity)). Similar to derivation on top p. 4656 of the Schork reference.

MATHEMATICA

a[n_] := Sum[(-1)^k FactorialPower[k, 2]^n/k!, {k, 2, Infinity}]*E; Array[a, 18] (* Jean-Fran├žois Alcover, Sep 01 2016 *)

CROSSREFS

Cf. -A000587(n) from Stirling2 case A008277 with a(0) := -1. A020556 (non-alternating sum, generalized Bell-numbers).

Sequence in context: A189438 A297586 A196576 * A274725 A250143 A069594

Adjacent sequences:  A090208 A090209 A090210 * A090212 A090213 A090214

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Dec 01 2003

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 May 27 20:36 EDT 2020. Contains 334667 sequences. (Running on oeis4.)