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A119390 a(n) = n!*Sum_{k=0..n} (-1)^(n-k)*Stirling1(n,k)/k!. 2
1, 1, 3, 22, 301, 6631, 214681, 9600088, 566959457, 42745927717, 4006577981071, 457002288429666, 62332395019232053, 10018273615964100787, 1873929413170092413773, 403602063302844878730196, 99165966659478338987124481, 27570715036265111940880945673, 8611670013649050886554308425147, 3002629280961610435928764405429774, 1161987842547239267511188646916322781 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

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 *)

CROSSREFS

Cf. A001569.

Sequence in context: A325295 A298693 A326430 * A271848 A144681 A305963

Adjacent sequences:  A119387 A119388 A119389 * A119391 A119392 A119393

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jul 25 2006

EXTENSIONS

More terms from Stefan Steinerberger, Nov 23 2007

STATUS

approved

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Last modified September 16 12:25 EDT 2021. Contains 347472 sequences. (Running on oeis4.)