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.
Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).
FORMULA
a(n) = A008277(n, 6) (Stirling2 triangle).
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved
