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A072678
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Generalized Bell numbers B_{4,2}.
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1
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1, 21, 1045, 93289, 12975561, 2581284541, 693347907421, 241253367679185, 105394372192969489, 56410454014314490981, 36271084122927079387941, 27567930377271475039277881, 24435533594428382909107147225
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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
| a(n)=(2*n)!*hypergeom([2*n+1], [3], 1)/(2*exp(1)), n=1, 2, ... Special values of the confluent hypergeometric function 1F1.
a(n)=sum(A090438(n, k), k=2..2*n)= sum((1/k!)*product(fallfac(k+(j-1)*(4-2), 2), j=1..n), k=1..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=4, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle). a(0) := 1 may be added.
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CROSSREFS
| Cf. A090439 (alternating row sums of A090438).
Sequence in context: A004704 A138473 A186392 * A012153 A143003 A193156
Adjacent sequences: A072675 A072676 A072677 * A072679 A072680 A072681
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KEYWORD
| nonn
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AUTHOR
| Karol A. Penson (penson(AT)lptl.jussieu.fr), Jul 01 2002
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EXTENSIONS
| Edited by Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Dec 23 2003
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