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A006260 Second-order Eulerian numbers <<n,3>>.
(Formerly M5162)
6
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; text; internal format)
OFFSET

3,2

REFERENCES

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).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 3..1000

I. Gessel and R. P. Stanley, Stirling polynomials, J. Combin. Theory, A 24 (1978), 24-33.

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). [Johannes W. Meijer, Oct 16 2009].

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);

CROSSREFS

a(n) = A008517(n, 4).

3rd column of A201637.

Equals for n=>4 fifth right hand column of A163936. [Johannes W. Meijer, Oct 16 2009].

Sequence in context: A231318 A083195 A004358 * A187625 A024303 A060195

Adjacent sequences:  A006257 A006258 A006259 * A006261 A006262 A006263

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

EXTENSIONS

More terms from Emeric Deutsch, Dec 15 2004

STATUS

approved

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Last modified October 15 08:45 EDT 2018. Contains 316210 sequences. (Running on oeis4.)