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A005583
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Coefficients of Chebyshev polynomials.
(Formerly M1999)
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5
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2, 11, 36, 91, 196, 378, 672, 1122, 1782, 2717, 4004, 5733, 8008, 10948, 14688, 19380, 25194, 32319, 40964, 51359, 63756, 78430, 95680, 115830, 139230, 166257, 197316, 232841, 273296, 319176, 371008, 429352, 494802, 567987, 649572, 740259, 840788
(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-5) is equal to the number of (n-5)-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..172
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)^6.
a(n)=binomial(n+4, n-1)+binomial(n+3, n-1)=(1/120)*n*(n+9)*(n+3)*(n+2)*(n+1).
Binomial(n,5)+2*binomial(n,4), n>=4. Binomial(n+2,5)-binomial(n,3), n>=4. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 21 2006
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MAPLE
| [seq(binomial(n+2, 5)-binomial(n, 3), n=4..45)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 21 2006
seq((n+5)*binomial(n, 5)/n, n=5..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 28 2007
A005583:=-(-2+z)/(z-1)**6; [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[n (n + 1) (n + 2) (n + 3)/4!, {n, 1, 60}] + Table[n (n + 1) (n + 2) (n + 3) (n + 4)/5!, {n, 1, 60}] (* From Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
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PROG
| (PARI) conv(u, v)=local(w); w=vector(length(u), i, sum(j=1, i, u[j]*v[i+1-j])); w; t(n)=n*(n+1)/2; u=vector(10, i, t(i)); v=vector(10, i, t(i)-1); conv(u, v)
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CROSSREFS
| Cf. A000217, A051747, A000389.
Sequence in context: A154416 A184538 A071244 * A176916 A015519 A096977
Adjacent sequences: A005580 A005581 A005582 * A005584 A005585 A005586
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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.
More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 21 2006
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