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A005584
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Coefficients of Chebyshev polynomials.
(Formerly M2059)
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5
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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; internal format)
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OFFSET
| 1,1
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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 R. Janjic (agnus(AT)blic.net), Jul 30 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. 797.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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].
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.
C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
Index entries for sequences related to Chebyshev polynomials.
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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 (zerinvarylajos(AT)yahoo.com), Jul 26 2006
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MAPLE
| [seq(binomial(n, 6)+2*binomial(n, 5), n=5..35)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 26 2006
A005584:=(-2+z)/(z-1)**7; [S. Plouffe in his 1992 dissertation.]
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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}] (* From Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
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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
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CROSSREFS
| Sequence in context: A117717 A176060 A168172 * A072416 A056305 A056297
Adjacent sequences: A005581 A005582 A005583 * A005585 A005586 A005587
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 07 1999.
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