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Search: id:A068939
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| A068939 |
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Bell(n^2), where Bell(n) are the Bell numbers, cf. A000110. |
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+0
2
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| 1, 1, 15, 21147, 10480142147, 4638590332229999353, 3819714729894818339975525681317, 10726137154573358400342215518590002633917247281
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n) = EXP(-1)*sum(k=>0, k^(n^2)/k!). - Benoit Cloitre (benoit7848c(AT)orange.fr), May 19 2002
Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)=int(x^n*(sum(exp(-ln(x)^2/(4*ln(k)))/(k!*sqrt(ln(k))), k=2..infinity)/(2*exp(1)*sqrt(Pi)*x)+Dirac(1-x)/exp(1)), x=0..infinity), n=0, 1...
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PROGRAM
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(PARI) for(n=0, 50, print1(round(sum(i=0, 1000, i^(n^2)/(i)!)/exp(1)), ", "))
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CROSSREFS
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Cf. A000110.
Sequence in context: A140285 A112614 A068732 this_sequence A104682 A013756 A078185
Adjacent sequences: A068936 A068937 A068938 this_sequence A068940 A068941 A068942
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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), Mar 08 2002
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