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%I M5162 #28 Aug 11 2018 02:56:13
%S 0,24,444,4400,32120,195800,1062500,5326160,25243904,114876376,
%T 507259276,2189829808,9292526920,38917528600,161343812980,
%U 663661077072,2713224461136,11039636532120,44751359547420,180880752056880
%N Second-order Eulerian numbers <<n,3>>.
%D R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, 2nd edition. Addison-Wesley, Reading, MA, 1994, p. 270.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seiichi Manyama, <a href="/A006260/b006260.txt">Table of n, a(n) for n = 3..1000</a>
%H I. Gessel and R. P. Stanley, <a href="https://doi.org/10.1016/0097-3165(78)90042-0">Stirling polynomials</a>, J. Combin. Theory, A 24 (1978), 24-33.
%F G.f.: x^4(24-36x-280x^2+652x^3-168x^4-288x^5)/((1-x)^4(1-2x)^3(1-3x)^2(1-4x)). - _Michael Somos_, Oct 13, 2002
%F a(n) = sum((-1)^(n+k+2)*binomial(2*n+1,k)*stirling1(2*n-k-3,n-k-3), k=0..n-4). [_Johannes W. Meijer_, Oct 16 2009].
%p G:=x^4*(24-36*x-280*x^2+652*x^3-168*x^4-288*x^5)/((1-x)^4*(1-2*x)^3*(1-3*x)^2*(1-4*x)): Gser:=series(G,x=0,27): seq(coeff(Gser,x^n),n=3..25);
%Y a(n) = A008517(n, 4).
%Y 3rd column of A201637.
%Y Equals for n=>4 fifth right hand column of A163936. [_Johannes W. Meijer_, Oct 16 2009].
%K nonn,easy
%O 3,2
%A _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_
%E More terms from _Emeric Deutsch_, Dec 15 2004
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