%I A064856
%S A064856 1,1,3,12,59,338,2185,15613,121553,1020170,9154963,87276995,879242215,
%T A064856 9319182044,103537712361,1201967382478,14540040004755,182840037042560,
%U A064856 2384985091689409,32209645344213417,449608555748234353
%N A064856 Stirling transform of Catalan numbers: a(n)=sum(stirling2(n,'k')*binomial(2*'k',
               'k')/('k'+1),'k'=0..n).
%F A064856 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...
%F A064856 E.g.f.: hypergeom([1/2], [2], 4*(exp(x)-1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Sep 11 2003
%Y A064856 Cf. A000108.
%Y A064856 Sequence in context: A126959 A058861 A105668 this_sequence A080337 A101054 
               A122752
%Y A064856 Adjacent sequences: A064853 A064854 A064855 this_sequence A064857 A064858 
               A064859
%K A064856 nice,nonn
%O A064856 0,3
%A A064856 Karol A. Penson (penson(AT)lptl.jussieu.fr), Oct 08 2001