%I #19 Aug 05 2024 04:14:45
%S 1,-6,21,-56,126,-252,463,-804,1365,-2366,4368,-8736,18565,-40410,
%T 87381,-184604,379050,-758100,1486675,-2884776,5592405,-10919090,
%U 21572460,-43144920,87087001,-176565486,357913941,-723002336
%N Expansion of bracket function.
%H G. C. Greubel, <a href="/A006090/b006090.txt">Table of n, a(n) for n = 0..1000</a>
%H H. W. Gould, <a href="http://www.fq.math.ca/Scanned/2-4/gould.pdf">Binomial coefficients, the bracket function and compositions with relatively prime summands</a>, Fib. Quart. 2, issue 4, (1964), 241-260.
%H <a href="/A005589/a005589.pdf">Problems Drive</a>, Eureka, 37 (1974), 8-11, 32-33, 24-27. (Annotated scanned copy)
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-6,-15,-20,-15,-6).
%F G.f.: 1/((1+x)^6-x^6).
%F a(n) = (-1)^n * Sum_{k=0..floor(n/6)} binomial(n+5,6*k+5). - _Seiichi Manyama_, Aug 05 2024
%t CoefficientList[Series[1/((1+x)^6-x^6),{x,0,30}],x] (* or *) LinearRecurrence[ {-6,-15,-20,-15,-6},{1,-6,21,-56,126},31] (* _Harvey P. Dale_, Oct 14 2016 *)
%o (PARI) x='x+O('x^50); Vec(1/((1+x)^6-x^6)) \\ _G. C. Greubel_, Jul 02 2017
%Y Column 6 of A307047.
%Y Cf. A000748, A000749, A000750, A001659.
%K sign
%O 0,2
%A _David Callan_