This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A008278 Triangle of Stirling numbers of 2nd kind, S(n,n-k+1), n >= 1, 1<=k<=n. 16
 1, 1, 1, 1, 3, 1, 1, 6, 7, 1, 1, 10, 25, 15, 1, 1, 15, 65, 90, 31, 1, 1, 21, 140, 350, 301, 63, 1, 1, 28, 266, 1050, 1701, 966, 127, 1, 1, 36, 462, 2646, 6951, 7770, 3025, 255, 1, 1, 45, 750, 5880, 22827, 42525, 34105, 9330 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS O.g.f. for the k-th column sequence is 1/(1-x) if k=1 and A(k,x):=((x^k)/(1-x)^(2*k+1))*sum(A008517(k,m+1)*x^m,m=0..k-1) if k>=2. A008517 is the second-order Eulerian triangle. Cf. p. 257, eq. (6.43) of the R. L. Graham et al. book. Wolfdieter Lang, Oct 14 2005. E.g.f. for the k-th column sequence with offset n=0 is E(k,x):= exp(x)*sum(A112493(k-1,m)*(x^(k-1+m))/(k-1+m)!,m=0..k-1) if k>=1. W. Lang, Oct 14 2005. The n-th row also gives the coefficients of the sigma polynomial of the empty graph \bar K_n. - Eric W. Weisstein, Apr 07 2017 The n-th row also gives the coefficients of the independence polynomial of the (n-1)-triangular honeycomb bishop graph. - Eric W. Weisstein, Apr 03 2018 REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 835. F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 223. R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, 2nd ed., 1994. LINKS T. D. Noe, Rows n=0..100 of triangle, flattened M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. T. Copeland, Generators, Inversion, and Matrix, Binomial, and Integral Transforms, 2015 U. N. Katugampola, A new Fractional Derivative and its Mellin Transform, arXiv preprint arXiv:1106.0965 [math.CA], 2011. Eric Weisstein's World of Mathematics, Bell Polynomial Eric Weisstein's World of Mathematics, Empty Graph Eric Weisstein's World of Mathematics, Independence Polynomial Eric Weisstein's World of Mathematics, Sigma Polynomial Eric Weisstein's World of Mathematics, Stirling Number of the Second Kind FORMULA a(n, k)=0 if n

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 21 11:52 EDT 2018. Contains 313939 sequences. (Running on oeis4.)