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Search: id:A070531
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| A070531 |
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Generalized Bell numbers B_{4,3}. |
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+0
3
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| 1, 73, 16333, 8030353, 7209986401, 10541813012041, 23227377813664333, 72925401604382826913, 312727862321385812968033
(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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In Maple notation, a(n)=(1/12)*n!*(n+1)!*(n+2)!*hypergeom([n+1, n+2, n+3], [2, 3, 4], 1)/exp(1)).
a(n)=sum(A090440(n, k), k=3..3*n)= sum((1/k!)*product(fallfac(k+(j-1)*(4-3), 3), j=1..n), k=3..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=4, s=3. 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. A091028 (alternating row sums of A090440).
Sequence in context: A116241 A105322 A091757 this_sequence A076848 A000319 A033394
Adjacent sequences: A070528 A070529 A070530 this_sequence A070532 A070533 A070534
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KEYWORD
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nonn
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AUTHOR
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Karol A. Penson (penson(AT)lptl.jussieu.fr), May 02 2002
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EXTENSIONS
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Edited by Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Dec 23 2003
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