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A000582
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Binomial coefficients C(n,9).
(Formerly M4712 N2013)
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20
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1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48620, 92378, 167960, 293930, 497420, 817190, 1307504, 2042975, 3124550, 4686825, 6906900, 10015005, 14307150, 20160075, 28048800, 38567100, 52451256, 70607460, 94143280
(list; graph; refs; listen; history; internal format)
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OFFSET
| 9,2
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COMMENTS
| Figurate numbers based on 9-dimensional regular simplex. - jvospost3(AT)gmail.com (jvospost3(AT)gmail.com), Nov 28 2004
a(n) = -A110555(n+1,9). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 27 2005
Product of 9 consecutive numbers divided by 9! - Artur Jasinski (grafix(AT)csl.pl), Dec 02 2007
In this sequence there are no primes - Artur Jasinski (grafix(AT)csl.pl), Dec 02 2007
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=9..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 259
Milan Janjic, Two Enumerative Functions
H. K. Kim, On Regular Polytope Numbers, Journal: Proc. Amer. Math. Soc. 131 (2003), 65-75, as PDF file.
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000.
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FORMULA
| G.f.: x^9/(1-x)^10
a(n+8)=n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)/9! - Artur Jasinski (grafix(AT)csl.pl), Dec 02 2007, R. J. Mathar, Jul 07 2009
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MAPLE
| A000582 := n->binomial(n, 9);
A000582:=1/(z-1)**10; [S. Plouffe in his 1992 dissertation for offset 0.]
seq(binomial(n, 9), n=0..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 23 2008, R. J. Mathar, Jul 07 2009
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MATHEMATICA
| Table[n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)/9!, {n, 1, 100}] - Artur Jasinski (grafix(AT)csl.pl), Dec 02 2007
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CROSSREFS
| Cf. A053138, A053131, A000581, A035927.
Sequence in context: A008492 A023035 A128936 * A145459 A034241 A022575
Adjacent sequences: A000579 A000580 A000581 * A000583 A000584 A000585
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KEYWORD
| easy,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 23 2000
Formulas referring to other offsets rewritten by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 07 2009
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