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A006976 Coefficients of Chebyshev polynomials.
(Formerly M4907)
9
1, 13, 98, 560, 2688, 11424, 44352, 160512, 549120, 1793792, 5637632, 17145856, 50692096, 146227200, 412778496, 1143078912, 3111714816, 8341487616, 22052208640, 57567870976, 148562247680, 379364311040, 959384125440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A069039. - Paul Barry, Feb 19 2003

If X_1, X_2, ..., X_n are 2-blocks of a (2n+1)-set X then, for n >= 5, a(n-5) is the number of (n+6)-subsets of X intersecting each X_i, (i = 1, 2, ..., n). - Milan Janjic, Nov 18 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. 795.

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

LINKS

Table of n, a(n) for n=0..22.

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].

Milan Janjic, Two Enumerative Functions

Index entries for sequences related to Chebyshev polynomials.

FORMULA

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

a(n) = 2^n*binomial(n+5,5) * (n+12)/12.

a(n) = 2^n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+12)/1440.

a(n) = sum{k = 0..floor((n+12)/2), C(n+12,2*k)*C(k,6) }. - Paul Barry, May 15 2003

a(n) = 2^(n-1)/6*binomial(n+5,5)*(n+12). - Brad Clardy, Mar 10 2012

PROG

(MAGMA) [2^(n-1)/6*Binomial(n+5, 5)*(n+12) : n in [0..25]]; // Brad Clardy, Mar 10 2012

CROSSREFS

a(n) = A039991(n+12, 12).

Partial sums are in A002409.

Sequence in context: A228680 A158795 A075899 * A282992 A295271 A034270

Adjacent sequences:  A006973 A006974 A006975 * A006977 A006978 A006979

KEYWORD

nonn,easy

AUTHOR

Simon Plouffe

EXTENSIONS

More terms from James A. Sellers, Aug 21 2000

STATUS

approved

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Last modified July 15 16:09 EDT 2019. Contains 325049 sequences. (Running on oeis4.)