A119391 - OEIS

%I #11 May 29 2020 07:22:58

%S 1,1,-1,4,-35,531,-12299,400534,-17277791,940844701,-61860211829,

%T 4667574681056,-372379676442971,24837948160750999,826269488792753097,

%U -1174087941563072053454,497371695628704851927041,-188274182030170078547881991,72347643557171655842626735159

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

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

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

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

%Y Cf. A001569, A119390.

%K easy,sign

%O 0,4

%A _Vladeta Jovovic_, Jul 25 2006

%E More terms from _Stefan Steinerberger_, Nov 23 2007