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A101053
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a(n) = n!*Sum_{k=0..n} Bell(k)/k! (cf. A000110).
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1
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1, 2, 6, 23, 107, 587, 3725, 26952, 219756, 1998951, 20105485, 221838905, 2666280457, 34689290378, 485840964614, 7288997427755
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Sequence was originally defined as an infinite sum involving generalized Laguerre polynomials: a(n)= ((-1)^n*n!/exp(1))*sum(LaguerreL(n,-n-1,k)/k!, k=0..infinity), n=0,1... . It appears in the problem of normal ordering of functions of boson operators. E.g.f: exp(exp(x)-1)/(1-x)
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MAPLE
| a:=n->sum(bell(j)*n!/j!, j=0..n):seq(a(n), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2007
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CROSSREFS
| Sequence in context: A113226 A071075 A007555 * A155857 A071076 A112501
Adjacent sequences: A101050 A101051 A101052 * A101054 A101055 A101056
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KEYWORD
| nonn
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AUTHOR
| Karol A. Penson (penson(AT)lptl.jussieu.fr), Nov 29 2004
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EXTENSIONS
| New definition from Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 01 2004
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