%I A119400
%S A119400 1,2,13,172,3809,126526,5874517,362848088,28744087297,2839192902874,
%T A119400 341922922464701,49297062811573732,8380916229314577313,
%U A119400 1658770724530766046422,378056469777362366873989
%N A119400 a(n) = Sum_{k=0..n} (n!/k!)^2*binomial(n,k).
%F A119400 Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*sqrt(x/(1-x)))/(1-x).
%t A119400 Table[Sum[(n!/k!)^2*Binomial[n, k], {k, 0, n}], {n, 0, 16}] - Stefan 
               Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 17 2007
%Y A119400 Sequence in context: A143851 A088316 A006905 this_sequence A137610 A073178 
               A062156
%Y A119400 Adjacent sequences: A119397 A119398 A119399 this_sequence A119401 A119402 
               A119403
%K A119400 easy,nonn
%O A119400 0,2
%A A119400 Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 25 2006
%E A119400 More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Jun 17 2007