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Search: id:A004301
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| A004301 |
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Second-order Eulerian numbers.
(Formerly M4265)
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+0
4
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| 0, 6, 58, 328, 1452, 5610, 19950, 67260, 218848, 695038, 2170626, 6699696, 20507988, 62407890, 189123286, 571432036, 1722945672, 5187185766, 15600353130
(list; graph; listen)
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OFFSET
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2,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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. Addison-Wesley, Reading, MA, 1990, p. 256.
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FORMULA
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G.f.: x^3(6-2x-12x^2)/((1-x)^3(1-2x)^2(1-3x)). a(n)=A008517(n, 3)=(9*3^n-(12+8*n)*2^n+(3+6*n+4*n^2))/2.. - Michael Somos, Oct 13, 2002
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)
a(n) = sum((-1)^(n+k)*binomial(2*n+1,k)*stirling1(2*n-k-2,n-k-2),k=0..n-3)
(End)
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PROGRAM
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(PARI) a(n)=if(n<0, 0, (9*3^n-(12+8*n)*2^n+(3+6*n+4*n^2))/2)
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CROSSREFS
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Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)
Equals the fourth right hand column of triangle A163936.
(End)
Sequence in context: A145170 A034218 A034237 this_sequence A073848 A141382 A034982
Adjacent sequences: A004298 A004299 A004300 this_sequence A004302 A004303 A004304
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)
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