A119390 - OEIS

%I #13 May 29 2020 07:30:00

%S 1,1,3,22,301,6631,214681,9600088,566959457,42745927717,4006577981071,

%T 457002288429666,62332395019232053,10018273615964100787,

%U 1873929413170092413773,403602063302844878730196,99165966659478338987124481,27570715036265111940880945673,8611670013649050886554308425147,3002629280961610435928764405429774,1161987842547239267511188646916322781

%N a(n) = n!*Sum_{k=0..n} (-1)^(n-k)*Stirling1(n,k)/k!.

%H Vaclav Kotesovec, <a href="/A119390/b119390.txt">Table of n, a(n) for n = 0..250</a>

%F Sum_{n>=0} a(n)*x^n/n!^2 = BesselJ(0,2*sqrt(log(1-x))).

%t Table[n!*Sum[(-1)^(n - k)*StirlingS1[n, k]/k!, {k, 0, n}], {n, 0, 20}] (* _Stefan Steinerberger_, Nov 23 2007 *)

%t CoefficientList[Series[BesselJ[0,2*Sqrt[Log[1-x]]], {x, 0, 20}], x] * Range[0, 20]!^2 (* _Vaclav Kotesovec_, Mar 02 2014 *)

%Y Cf. A001569.

%K easy,nonn

%O 0,3

%A _Vladeta Jovovic_, Jul 25 2006

%E More terms from _Stefan Steinerberger_, Nov 23 2007