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Search: id:A064856
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| A064856 |
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Stirling transform of Catalan numbers: a(n)=sum(stirling2(n,'k')*binomial(2*'k','k')/('k'+1),'k'=0..n). |
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+0
3
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| 1, 1, 3, 12, 59, 338, 2185, 15613, 121553, 1020170, 9154963, 87276995, 879242215, 9319182044, 103537712361, 1201967382478, 14540040004755, 182840037042560, 2384985091689409, 32209645344213417, 449608555748234353
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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E.g.f.: exp(2*exp(z)-2)*(BesselI(0, 2*exp(z)-2)-BesselI(1, 2*exp(z)-2)). Representation as a sum of an infinite series involving the confluent hypergeometric function 1F1, in Maple notation: a(n)=evalf(sum('k'^n*2^(2*'k')*GAMMA('k'+1/2)*evalf(hypergeom(['k'+1/2], ['k'+2], -4))/(sqrt(Pi)*'k'!*('k'+1)!), 'k'=0..infinity)), n=0, 1...
E.g.f.: hypergeom([1/2], [2], 4*(exp(x)-1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 11 2003
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CROSSREFS
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Cf. A000108.
Sequence in context: A126959 A058861 A105668 this_sequence A080337 A101054 A122752
Adjacent sequences: A064853 A064854 A064855 this_sequence A064857 A064858 A064859
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KEYWORD
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nice,nonn
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AUTHOR
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Karol A. Penson (penson(AT)lptl.jussieu.fr), Oct 08 2001
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