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A005583 Coefficients of Chebyshev polynomials.
(Formerly M1999)
7
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; text; internal format)
OFFSET

1,1

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 Janjic, Jul 30 2007

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..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].

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)^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, Jul 21 2006

MAPLE

[seq(binomial(n+2, 5)-binomial(n, 3), n=4..45)]; - Zerinvary Lajos, Jul 21 2006

seq((n+5)*binomial(n, 5)/n, n=5..41); - Zerinvary Lajos, Feb 28 2007

A005583:=-(-2+z)/(z-1)**6; [Simon Plouffe in his 1992 dissertation.]

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}] (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)

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)

CROSSREFS

Cf. A000217, A051747, A000389.

Sequence in context: A184538 A238706 A071244 * A176916 A015519 A096977

Adjacent sequences:  A005580 A005581 A005582 * A005584 A005585 A005586

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

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

More terms from Zerinvary Lajos, Jul 21 2006

STATUS

approved

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Last modified October 24 20:44 EDT 2014. Contains 248516 sequences.