

A001288


a(n) = binomial(n,11).
(Formerly M4850 N2073)


13



1, 12, 78, 364, 1365, 4368, 12376, 31824, 75582, 167960, 352716, 705432, 1352078, 2496144, 4457400, 7726160, 13037895, 21474180, 34597290, 54627300, 84672315, 129024480, 193536720, 286097760, 417225900, 600805296, 854992152, 1203322288, 1676056044
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OFFSET

11,2


COMMENTS

a(n) = A110555(n+1,11).  Reinhard Zumkeller, Jul 27 2005
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 npermutations (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.
A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 196.
Chinchon, A. S., Mixing Benford, GoogleVis And OnLine Encyclopedia of Integer Sequences, URL = https://fronkonstin.com/2014/12/23/mixingbendfordgooglevisandonlineencyclopediaofintegersequences/, 2014. Note: as of Feb 09 2017, the results in this page appear to be incorrect  N. J. A. Sloane, Feb 09 2017.
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.
Kenneth A Ross, First Digits of Squares and Cubes, Math. Mag. 85 (2012) 3642. doi:10.4169/math.mag.85.1.36.
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].
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 261
Milan Janjic, Two Enumerative Functions
Index entries for sequences related to Benford's law


FORMULA

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/(1x)^12. a(n) = binomial(n,11).  Zerinvary Lajos, Aug 06 2008, R. J. Mathar, Jul 07 2009


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 *)


CROSSREFS

Sequence in context: A162629 A008504 A008494 * A121665 A124863 A022577
Adjacent sequences: A001285 A001286 A001287 * A001289 A001290 A001291


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Some formulas for other offsets corrected by R. J. Mathar, Jul 07 2009


STATUS

approved



