%I M3851 N1576 #32 Feb 02 2021 20:45:56
%S 1,-5,15,-35,70,-125,200,-275,275,0,-1000,3625,-9500,21250,-42500,
%T 76875,-124375,171875,-171875,0,621875,-2250000,5890625,-13171875,
%U 26343750,-47656250,77109375,-106562500,106562500,0
%N Expansion of bracket function.
%C It appears that the (unsigned) sequence is identical to its 5th-order absolute difference. - _John W. Layman_, Sep 23 2003
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seiichi Manyama, <a href="/A000750/b000750.txt">Table of n, a(n) for n = 0..3000</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(4) (1964), 241-260.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-5, -10, -10, -5).
%F G.f.: 1/((1+x)^5-x^5).
%F a(n) = (-1)^n * Sum_{k=0..floor(n/5)} (-1)^k * binomial(n+4,5*k+4). - _Seiichi Manyama_, Mar 21 2019
%t LinearRecurrence[{-5, -10, -10, -5}, {1, -5, 15, -35}, 30] (* _Jean-François Alcover_, Feb 11 2016 *)
%o (PARI) Vec(1/((1+x)^5-x^5) + O(x^40)) \\ _Michel Marcus_, Feb 11 2016
%o (PARI) {a(n) = (-1)^n*sum(k=0, n\5, (-1)^k*binomial(n+4, 5*k+4))} \\ _Seiichi Manyama_, Mar 21 2019
%Y Column 5 of A307047.
%Y Cf. A000748, A000749, A001659, A006090, A049016.
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_