A006260 Second-order Eulerian numbers <<n,3>>. (Formerly M5162)

0, 24, 444, 4400, 32120, 195800, 1062500, 5326160, 25243904, 114876376, 507259276, 2189829808, 9292526920, 38917528600, 161343812980, 663661077072, 2713224461136, 11039636532120, 44751359547420, 180880752056880

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