login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005584 Coefficients of Chebyshev polynomials.
(Formerly M2059)
7
2, 13, 49, 140, 336, 714, 1386, 2508, 4290, 7007, 11011, 16744, 24752, 35700, 50388, 69768, 94962, 127281, 168245, 219604, 283360, 361790, 457470, 573300, 712530, 878787, 1076103, 1308944, 1582240, 1901416 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If X is an n-set and Y a fixed 2-subset of X then a(n-6) is equal to the number of (n-6)-subsets of X intersecting Y. - Milan Janjic, Jul 30 2007

a(n-1) = risefac(n+1,6)/6! - risefac(n+1,4)/4! is for n >=1 also the number of independent components of a symmetric traceless tensor of rank 6 and dimension n. Here risefac is the rising factorial. Put a(0) = 0. - 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. 797.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Milan Janjic, Two Enumerative Functions

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].

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.

Index entries for sequences related to Chebyshev polynomials.

FORMULA

G.f.: x*(2-x) / (1-x)^7.

a(n)=binomial(n+5, n-1)+binomial(n+4, n-1)=1/720*n*(n+11)*(n+4)*(n+3)*(n+2)*(n+1).

Binomial(n,6)+2*binomial(n,5), n>=5. - Zerinvary Lajos, Jul 26 2006

a(n+1) = A127672(12+n, n), n >= 0, where A127672 gives the coefficients of Chebyshev's C polynomials. See the Abramowitz-Stegun reference - Wolfdieter Lang, Dec 10 2015

MAPLE

[seq(binomial(n, 6)+2*binomial(n, 5), n=5..35)]; - Zerinvary Lajos, Jul 26 2006

A005584:=(-2+z)/(z-1)**7; [Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

Table[n (n + 1) (n + 2) (n + 3) (n + 4)/5!, {n, 1, 60}] + Table[n (n + 1) (n + 2) (n + 3) (n + 4) (n + 5)/6!, {n, 1, 60}] (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)

PROG

(PARI) a(n)=n*(n+11)*(n+4)*(n+3)*(n+2)*(n+1)/720 \\ Charles R Greathouse IV, Jun 14 2011

(MAGMA) [n*(n+11)*(n+4)*(n+3)*(n+2)*(n+1)/720: n in [1..40]]; // Vincenzo Librandi, Jun 15 2011

CROSSREFS

Cf. A127672, A005581, A005582, A005583.

Sequence in context: A176060 A168172 A270294 * A072416 A254784 A056305

Adjacent sequences:  A005581 A005582 A005583 * A005585 A005586 A005587

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 07 1999.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 19:05 EST 2016. Contains 278895 sequences.