OFFSET
11,2
COMMENTS
Product of 11 consecutive numbers divided by 11!. - Artur Jasinski, Dec 02 2007
In this sequence there are no primes. - Artur Jasinski, Dec 02 2007
With a different offset, number of n-permutations (n>=11) of 2 objects: u,v, with repetition allowed, containing exactly (11) u's. Example: n=11, a(0)=1 because we have uuuuuuuuuuu n=12, a(1)=12 because we have uuuuuuuuuuuv, uuuuuuuuuuvu, uuuuuuuuuvuu, uuuuuuuuvuuu, uuuuuuuvuuuu, uuuuuuvuuuuu, uuuuuvuuuuuu, uuuuvuuuuuuu, uuuvuuuuuuuu, uuvuuuuuuuuu uvuuuuuuuuuu, vuuuuuuuuuuu. - Zerinvary Lajos, Aug 06 2008
Does not satisfy Benford's law (because n^11 does not, see Ross, 2012). - N. J. A. Sloane, Feb 09 2017
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. 828.
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 196.
L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 7.
J. C. P. Miller, editor, Table of Binomial Coefficients. Royal Society Mathematical Tables, Vol. 3, Cambridge Univ. Press, 1954.
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=11..1000
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].
Peter J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
A. S. Chinchon, Mixing Benford, GoogleVis And On-Line Encyclopedia of Integer Sequences, 2014. Note: as of Feb 09 2017, the results in this page appear to be incorrect - N. J. A. Sloane, Feb 09 2017.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 261
Milan Janjic, Two Enumerative Functions.
Ângela Mestre, José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
Kenneth A. Ross, First Digits of Squares and Cubes, Math. Mag. 85 (2012) 36-42.
Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).
FORMULA
a(n) = -A110555(n+1,11). - Reinhard Zumkeller, Jul 27 2005
a(n+10) = n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)(n+9)(n+10)/11!. - Artur Jasinski, Dec 02 2007; R. J. Mathar, Jul 07 2009
G.f.: x^11/(1-x)^12. a(n) = binomial(n,11). - Zerinvary Lajos, Aug 06 2008; R. J. Mathar, Jul 07 2009
From Amiram Eldar, Dec 10 2020: (Start)
Sum_{n>=11} 1/a(n) = 11/10.
MAPLE
seq(binomial(n, 11), n=0..30); # Zerinvary Lajos, Aug 06 2008, R. J. Mathar, Jul 07 2009
MATHEMATICA
Table[n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)(n+9)(n+10)/11!, {n, 1, 100}] (* Artur Jasinski, Dec 02 2007 *)
Binomial[Range[11, 50], 11] (* Harvey P. Dale, Oct 02 2012 *)
PROG
(PARI) for(n=11, 50, print1(binomial(n, 11), ", ")) \\ G. C. Greubel, Aug 31 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Some formulas for other offsets corrected by R. J. Mathar, Jul 07 2009
STATUS
approved