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%I M3495 #41 Dec 02 2022 07:05:38
%S 4,15,52,151,372,799,1540,2727,4516,7087,10644,15415,21652,29631,
%T 39652,52039,67140,85327,106996,132567,162484,197215,237252,283111,
%U 335332,394479,461140,535927,619476,712447,815524,929415,1054852,1192591,1343412,1508119,1687540
%N From expansion of falling factorials.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H G. C. Greubel, <a href="/A005492/b005492.txt">Table of n, a(n) for n = 4..1004</a>
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H E. G. Whitehead, Jr., <a href="http://dx.doi.org/10.1016/0097-3165(78)90061-4">Stirling number identities from chromatic polynomials</a>, J. Combin. Theory, A 24 (1978), 314-317.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F a(n) = n^4 - 16*n^3 + 102*n^2 - 300*n + 340.
%F G.f.: x^4*(4-5*x+17*x^2+x^3+7*x^4)/(1-x)^5. - _Harvey P. Dale_, Dec 25 2012
%F E.g.f.: (1/6)*(-2040 - 762*x - 108*x^2 - 7*x^3 + (2040 - 1278*x + 366*x^2 - 60*x^3 + 6*x^4)*exp(x)). - _G. C. Greubel_, Dec 01 2022
%p A005492:=-(15-23*z+41*z**2-13*z**3+4*z**4)/(z-1)**5; # Conjectured by _Simon Plouffe_ in his 1992 dissertation. Gives sequence except for the leading 4.
%t LinearRecurrence[{5,-10,10,-5,1},{4,15,52,151,372},50] (* _Harvey P. Dale_, Dec 25 2012 *)
%o (Magma) [n^4 -16*n^3 +102*n^2 -300*n +340: n in [4..50]]; // _G. C. Greubel_, Dec 01 2022
%o (SageMath) [n^4 -16*n^3 +102*n^2 -300*n +340 for n in range(4,51)] # _G. C. Greubel_, Dec 01 2022
%Y Row n=4 of A108087 (shifted and first term prepended).
%Y Cf. A005490.
%K nonn,easy
%O 4,1
%A _N. J. A. Sloane_, _Simon Plouffe_
%E More terms from Pab Ter (pabrlos(AT)yahoo.com), May 09 2004
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