A000770 Stirling numbers of the second kind, S(n,6). (Formerly M5112 N2215)

1, 21, 266, 2646, 22827, 179487, 1323652, 9321312, 63436373, 420693273, 2734926558, 17505749898, 110687251039, 693081601779, 4306078895384, 26585679462804, 163305339345225, 998969857983405, 6090236036084530, 37026417000002430, 224595186974125331

Offset

6,2

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.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n=6..200

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].

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 349

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Formula

G.f.: x^6/product(1 - k*x, k = 1..6).

E.g.f.: ((exp(x) - 1)^6)/6!.

a(n) = 1/720*(6^n - 6*5^n + 15*4^n - 20*3^n + 15*2^n - 6). - Vaclav Kotesovec, Nov 19 2012

a(n) = det(|s(i+6,j+5)|, 1 <= i,j <= n-6), where s(n,k) are Stirling numbers of the first kind. - Mircea Merca, Apr 06 2013

Maple

A000770:=1/(z-1)/(6*z-1)/(4*z-1)/(3*z-1)/(2*z-1)/(5*z-1); # conjectured by Simon Plouffe in his 1992 dissertation

Mathematica

Table[1/720 * (6^n - 6 * 5^n + 15 * 4^n - 20 * 3^n + 15 * 2^n - 6), {n, 6, 20}] (* Vaclav Kotesovec, Nov 19 2012 *)
StirlingS2[Range[6, 25], 6] (* Alonso del Arte, Dec 07 2014 *)

Crossrefs

a(n)= A008277(n, 6) (Stirling2 triangle).

Cf. A008277.

Sequence in context: A092794 A133717 A056282 * A327507 A133105 A215766

Adjacent sequences: A000767 A000768 A000769 * A000771 A000772 A000773

Keyword

nonn

Author

N. J. A. Sloane

Status

approved