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Search: id:A091748
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| A091748 |
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Generalized Bell numbers B_{6,2}. |
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+0
4
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| 1, 43, 5083, 1160113, 432168721, 238012552651, 181520958432283, 182989529196234433, 235492729726705299073, 376560458072018837889931, 732162019709408940671604091, 1700645336651586566571229542193
(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(A091746(n, k), k=2..2*n)= sum((1/k!)*product(fallfac(k+4*(j-1), 2), j=1..n), k=2..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=6, 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. A072019 ( B_{5, 2}).
Sequence in context: A110704 A060485 A081795 this_sequence A147522 A155477 A125828
Adjacent sequences: A091745 A091746 A091747 this_sequence A091749 A091750 A091751
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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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