The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A320961 The exponential limit of (-x)!, rounded to the nearest integer. 0
 1, 1, 4, 27, 353, 6128, 145159, 4402407, 166608593, 7666343436, 420646243820, 27079750092637, 2018074017351900, 172131994564410026, 16641769389384512884, 1808431867178308597550, 219272140061011055068448, 29473880023661693302772550, 4366902281695075479226089449 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The exponential limit of a function is defined in A320956. Applied to (-x)! Maple returns a sequence of sums of Zeta values, powers of Pi, powers of Euler's gamma, etc.. The sequence starts: 1, gamma, (1/3)*Pi^2 + 2* gamma^2, 10*Zeta(3) + (5/2)*Pi^2*gamma + 5*gamma^3, ... These sums, rounded to the nearest integer, give the sequence. LINKS Table of n, a(n) for n=0..18. MAPLE explim := (len, f) -> seq(combinat:-bell(n)*((D@@n)(f))(0), n=0..len): explim(18, x -> (-x)!): map(round, [evalf(%, 46)]); MATHEMATICA m = 19; CoefficientList[(-x)!+O[x]^m, x]*Range[0, m-1]!*BellB[Range[0, m-1]] // Round (* Jean-François Alcover, Jul 21 2019 *) CROSSREFS Cf. A320956, A000142. The exponential limit of other functions: A320955 (exp), A320962 (log(x+1)), A320958 (arcsin), A320959 (arctanh). Sequence in context: A221411 A304654 A203202 * A239726 A058155 A334527 Adjacent sequences: A320958 A320959 A320960 * A320962 A320963 A320964 KEYWORD nonn AUTHOR Peter Luschny, Nov 07 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 12 10:47 EDT 2024. Contains 375850 sequences. (Running on oeis4.)