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Expansion of e.g.f.: exp(x)*sqrt(1-2x).
5

%I #20 Aug 30 2023 11:42:44

%S 1,0,-2,-8,-36,-224,-1880,-19872,-251888,-3712256,-62286624,

%T -1171487360,-24402416192,-557542291968,-13861636770176,

%U -372514645389824,-10759590258589440,-332386419622387712

%N Expansion of e.g.f.: exp(x)*sqrt(1-2x).

%H Vincenzo Librandi, <a href="/A055142/b055142.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) ~ -2^(n-1/2) * n^(n-1) / exp(n-1/2). - _Vaclav Kotesovec_, Mar 29 2014

%F D-finite with recurrence: a(n) +2*(-n+1)*a(n-1) +2*(n-1)*a(n-2)=0. - _R. J. Mathar_, Jan 22 2020

%t CoefficientList[Series[E^x*Sqrt[1-2*x], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Mar 29 2014 *)

%o (Sage)

%o def A055142(n):

%o @CachedFunction

%o def h(n):

%o return (-1)^n*2*(n-2)*abs(h(n-1)+h(n-2)) if n>1 else 1

%o return -(-1)^(n+1)*h(n+1)

%o [A055142(n) for n in (0..17)] # _Peter Luschny_, Nov 02 2012

%Y Cf. A001147, A053871.

%Y Column 0 of triangle A055141.

%K sign

%O 0,3

%A _Christian G. Bower_, May 09 2000