

A001287


Binomial coefficients C(n,10).
(Formerly M4794 N2046)


17



1, 11, 66, 286, 1001, 3003, 8008, 19448, 43758, 92378, 184756, 352716, 646646, 1144066, 1961256, 3268760, 5311735, 8436285, 13123110, 20030010, 30045015, 44352165, 64512240, 92561040, 131128140, 183579396, 254186856, 348330136, 472733756, 635745396
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OFFSET

10,2


COMMENTS

a(n) = A110555(n+1,10).  Reinhard Zumkeller, Jul 27 2005
Product of 10 consecutive numbers divided by 10!  Artur Jasinski, Dec 02 2007
In this sequence only 11 is prime.  Artur Jasinski, Dec 02 2007
With a different offset, number of npermutations (n>=10) of 2 objects: u,v, with repetition allowed, containing exactly 10 u's. Example: a(1)=11 because we have uuuuuuuuuuv, uuuuuuuuuvu, uuuuuuuuvuu, uuuuuuuvuuu, uuuuuuvuuuu, uuuuuvuuuuu, uuuuvuuuuuu, uuuvuuuuuuu, uuvuuuuuuuu, uvuuuuuuuuu and vuuuuuuuuuu.  Zerinvary Lajos, Aug 03 2008
a(9+k) is the number of times that each digit appears repeated inside a list made with all the possible base 10 numbers of k digits such that their digits are read in ascending order from left to right. R. J. Cano Jul 20 2014
a(n) = fallfac(n,10)/10! = binomial(n, 10) is also the number of independent components of an antisymmetric tensor of rank 10 and dimension n >= 10 (for n=1..9 this becomes 0). Here fallfac is the falling factorial.  Wolfdieter Lang, Dec 10 2015


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.
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 = 10..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 260
Milan Janjic, Two Enumerative Functions
Index entries for linear recurrences with constant coefficients, signature (11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1).


FORMULA

a(n+9) = n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)(n+9)/10!.  Artur Jasinski, Dec 02 2007, R. J. Mathar, Jul 07 2009
G.f.: x^10/(1x)^11.  Zerinvary Lajos, Aug 06 2008, R. J. Mathar, Jul 07 2009
Sum_{k>=10} 1/a(k) = 10/9.  Tom Edgar, Sep 10 2015


MAPLE

seq(binomial(n, 10), n=10..31); # Zerinvary Lajos, Aug 06 2008


MATHEMATICA

Table[n (n + 1) (n + 2) (n + 3) (n + 4) (n + 5) (n + 6) (n + 7) (n + 8) (n + 9)/10!, {n, 1, 100}] (* Artur Jasinski, Dec 02 2007 *)
Table[Binomial[n, 10], {n, 10, 20}] (* Zerinvary Lajos, Jan 31 2010 *)


PROG

(MAGMA) [Binomial(n, 10): n in [10..40]]; // Vincenzo Librandi, Sep 11 2015
(PARI) a(n)=binomial(n, 10) \\ Charles R Greathouse IV, Sep 24 2015
(Python)
A001287_list, m = [], [1]*11
for _ in range(10**2):
A001287_list.append(m[1])
for i in range(10):
m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016


CROSSREFS

Sequence in context: A247610 A008503 A008493 * A229891 A243745 A221143
Adjacent sequences: A001284 A001285 A001286 * A001288 A001289 A001290


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

Formulas valid for different offsets rewritten by R. J. Mathar, Jul 07 2009
Extended by Ray Chandler, Oct 25 2011


STATUS

approved



