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A006260
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Second-order Eulerian numbers <<n,3>>.
(Formerly M5162)
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2
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0, 24, 444, 4400, 32120, 195800, 1062500, 5326160, 25243904, 114876376, 507259276, 2189829808, 9292526920, 38917528600, 161343812980, 663661077072, 2713224461136, 11039636532120, 44751359547420, 180880752056880
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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REFERENCES
| I. Gessel and R. P. Stanley, Stirling polynomials, J. Combin. Theory, A 24 (1978), 24-33.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, 2nd edition. Addison-Wesley, Reading, MA, 1994, p. 270.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| 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
a(n) = sum((-1)^(n+k+2)*binomial(2*n+1,k)*stirling1(2*n-k-3,n-k-3), k=0..n-4) [From Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009].
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MAPLE
| 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);
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CROSSREFS
| a(n)=A008517(n, 4).
Equals for n=>4 fifth right hand column of A163936 [From Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009].
Sequence in context: A062149 A083195 A004358 * A187625 A024303 A060195
Adjacent sequences: A006257 A006258 A006259 * A006261 A006262 A006263
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 15 2004
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