A090218 Alternating row sums of array A090216 (generalized Stirling2 array S_{5,5}(n,m)).

1, -56, -29809, 326279119, -2175016082574, -74839638000014951, 12021284427301302745281, -1570241381612307786517290066, 198470943846200888426002717105781, 5344440525443920698933785031734661899, -41721146701452069718231186424275967809608724

Offset: 1

Author

Wolfdieter Lang, Dec 01 2003

Keywords

• sign
• easy

References

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

Formula

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.

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.