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Search: id:A090218
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| A090218 |
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Alternating row sums of array A090216 (generalized Stirling2 array S_{5,5}(n,m)). |
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+0
2
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| 1, -56, -29809, 326279119, -2175016082574, -74839638000014951, 12021284427301302745281, -1570241381612307786517290066, 198470943846200888426002717105781, 5344440525443920698933785031734661899, -41721146701452069718231186424275967809608724
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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M. Schork, On the combinatorics of normal ordering bosonic operators and deforming it, J. Phys. A 36 (2003) 4651-4665.
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FORMULA
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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.
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CROSSREFS
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Adjacent sequences: A090215 A090216 A090217 this_sequence A090219 A090220 A090221
Sequence in context: A059989 A059073 A115469 this_sequence A009837 A093256 A135315
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KEYWORD
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sign,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Dec 01 2003
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