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Search: id:A091757
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| A091757 |
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Generalized Bell numbers B_{8,2}. |
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+0
3
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| 1, 73, 15945, 6993073, 5124715761, 5641397595321, 8700819552421753, 17898786381229403105, 47345052327747786859873, 156535091017683923932912041, 632460052562874236182866885161
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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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.
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FORMULA
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a(n)=sum(A092077(n, k), k=2..2*n)= sum((1/k!)*product(fallfac(k+6*(j-1), 2), j=1..n), k=2..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=8, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle). a(0) := 1 may be added.
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CROSSREFS
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Cf. A091749 (B_{7, 2}).
Sequence in context: A089788 A116241 A105322 this_sequence A070531 A076848 A000319
Adjacent sequences: A091754 A091755 A091756 this_sequence A091758 A091759 A091760
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 27 2004
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