%I #3 Oct 12 2012 14:40:19

%S 1,-56,-29809,326279119,-2175016082574,-74839638000014951,

%T 12021284427301302745281,-1570241381612307786517290066,

%U 198470943846200888426002717105781,5344440525443920698933785031734661899,-41721146701452069718231186424275967809608724

%N Alternating row sums of array A090216 (generalized Stirling2 array S_{5,5}(n,m)).

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

%F a(n) = -sum(((-1)^k)*(fallfac(k, 5)^n)/k!, k=5..infinity)*exp(1), with fallfac(k, 5)=A008279(k, 5)=product(k+1-r, r=1..5) and n>=1. This produces also a(0)=-1.

%F E.g.f. if a(0)=-1 is added: -exp(1)*(sum(((-1)^k)*exp(fallfac(k, 5)*x)/k!, k=5..infinity) + 3/8). 3/8=A000166(4)/4! with the subfactorials A000166. Similar to the derivation on top of p. 4656 of the Schork reference.

%K sign,easy

%O 1,2

%A _Wolfdieter Lang_, Dec 01 2003