OFFSET
7,2
COMMENTS
G.f.: x^7/product(1-k*x,k=1..7). E.g.f.: ((exp(x)-1)^7)/7!.
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=7..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 350
Index entries for linear recurrences with constant coefficients, signature (28,-322,1960,-6769,13132,-13068,5040).
FORMULA
a(n) = A008277(n, 7) (Stirling2 triangle).
a(n) = 1/720*(7^(n-1)-6^n+3*5^n-5*4^n+5*3^n-3*2^n+1). - Vaclav Kotesovec, Nov 19 2012
a(n) = det(|s(i+7,j+6)|, 1 <= i,j <= n-7), where s(n,k) are Stirling numbers of the first kind. - Mircea Merca, Apr 06 2013
MATHEMATICA
lst={}; Do[f=StirlingS2[n, 7]; AppendTo[lst, f], {n, 7, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)
CoefficientList[Series[1/((1 - x) (1 - 2 x) (1 - 3 x) (1 - 4 x) (1 - 5 x) (1 - 6 x) (1 - 7 x)), {x, 0, 25}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)
Table[1/720*(7^(n-1)-6^n+3*5^n-5*4^n+5*3^n-3*2^n+1), {n, 7, 20}] (* Vaclav Kotesovec, Nov 19 2012 *)
LinearRecurrence[{28, -322, 1960, -6769, 13132, -13068, 5040}, {1, 28, 462, 5880, 63987, 627396, 5715424}, 20] (* or *) Drop[StirlingS2[Range[30], 7], 6] (* Harvey P. Dale, Jul 25 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Two more terms from Neven Juric, Oct 22 2009
Definition corrected by Vaclav Kotesovec, Nov 19 2012
STATUS
approved