A006260 Second-order Eulerian numbers <>.

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

Offset: 3

Author

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

Keywords

• nonn
• easy

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.

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].

Programs

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);

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].

Extensions

More terms from Emeric Deutsch, Dec 15 2004