A119390 a(n) = n!*Sum_{k=0..n} (-1)^(n-k)*Stirling1(n,k)/k!.

1, 1, 3, 22, 301, 6631, 214681, 9600088, 566959457, 42745927717, 4006577981071, 457002288429666, 62332395019232053, 10018273615964100787, 1873929413170092413773, 403602063302844878730196, 99165966659478338987124481, 27570715036265111940880945673, 8611670013649050886554308425147, 3002629280961610435928764405429774, 1161987842547239267511188646916322781

Offset: 0

Author

Vladeta Jovovic, Jul 25 2006

Keywords

• easy
• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A001569.

Programs

Mathematica

Table[n!*Sum[(-1)^(n - k)*StirlingS1[n, k]/k!, {k, 0, n}], {n, 0, 20}] (* Stefan Steinerberger, Nov 23 2007 *)
CoefficientList[Series[BesselJ[0,2*Sqrt[Log[1-x]]], {x, 0, 20}], x] * Range[0, 20]!^2 (* Vaclav Kotesovec, Mar 02 2014 *)

Formula

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

Extensions

More terms from Stefan Steinerberger, Nov 23 2007