This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A090211 #8 Sep 01 2016 10:22:38
%S A090211 1,-1,-1,41,-375,-3001,177063,-990543,-144800527,3644593711,
%T A090211 214013895023,-12488200175463,-553322483517383,61495192102867639,
%U A090211 2469939623420627543,-448608666325921194271,-19104207797417792353951,4742067751530355028847327
%N A090211 Alternating row sums of array A078739 ((2,2)-Stirling2).
%D A090211 P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.
%D A090211 M. Schork, On the combinatorics of normal ordering bosonic operators and deforming it, J. Phys. A 36 (2003) 4651-4665.
%H A090211 P. Blasiak, K. A. Penson and A. I. Solomon, <a href="http://www.arXiv.org/abs/quant-ph/0402027">The general boson normal ordering problem.</a>
%F A090211 a(n) := sum( A078739(n, m)*(-1)^m, m=2..2*n), n>=1. a(0) := +1 may be added.
%F A090211 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.
%F A090211 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.
%t A090211 a[n_] := Sum[(-1)^k FactorialPower[k, 2]^n/k!, {k, 2, Infinity}]*E; Array[a, 18] (* _Jean-François Alcover_, Sep 01 2016 *)
%Y A090211 Cf. -A000587(n) from Stirling2 case A008277 with a(0) := -1. A020556 (non-alternating sum, generalized Bell-numbers).
%K A090211 sign,easy
%O A090211 1,4
%A A090211 _Wolfdieter Lang_, Dec 01 2003