A119391 a(n) = n!*Sum_{k=0..n} Stirling1(n,k)/k!.

1, 1, -1, 4, -35, 531, -12299, 400534, -17277791, 940844701, -61860211829, 4667574681056, -372379676442971, 24837948160750999, 826269488792753097, -1174087941563072053454, 497371695628704851927041, -188274182030170078547881991, 72347643557171655842626735159

Offset: 0

Author

Vladeta Jovovic, Jul 25 2006

Keywords

• easy
• sign

Crossrefs

Cf. A001569, A119390.

Programs

Mathematica

Table[n!*Sum[StirlingS1[n, k]/k!, {k, 0, n}], {n, 0, 20}] (* Stefan Steinerberger, Nov 23 2007 *)
CoefficientList[Series[BesselI[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 = BesselI(0,2*sqrt(log(1+x))).

Extensions

More terms from Stefan Steinerberger, Nov 23 2007