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The sequence 2^(1-n)*a(n) is fixed (up to signs) by Stirling2 transform.
(Formerly M3670)
177

%I M3670 #24 Jan 25 2020 17:58:00

%S 1,-1,1,4,-38,-78,5246,-11680,-2066056,22308440,1898577048,

%T -48769559680,-3518093351728,174500124820560,11809059761527536,

%U -1021558531563834368,-66133927485154902144,9433326815405995274624,578173001867228425792384

%N The sequence 2^(1-n)*a(n) is fixed (up to signs) by Stirling2 transform.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F The e.g.f. for the latter sequence satisfies A(x) + A(e^x - 1 ) = 2.

%e The sequence that is fixed up to signs by STIRLING2 is 1, -1/2, 1/4, 4/8, -38/16, -78/32, 5246/64, ...

%K sign,eigen

%O 1,4

%A _N. J. A. Sloane_, _Mira Bernstein_

%E More terms from _Vladeta Jovovic_, Jul 12 2001