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A006975 Coefficients of Chebyshev polynomials.
(Formerly M4796)
10
1, 11, 72, 364, 1568, 6048, 21504, 71808, 228096, 695552, 2050048, 5870592, 16400384, 44843008, 120324096, 317521920, 825556992, 2118057984, 5369233408, 13463453696, 33426505728, 82239815680, 200655503360, 485826232320 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A069038. - Paul Barry, Feb 19 2003

If X_1, X_2, ..., X_n are 2-blocks of a (2n+1)-set X then, for n>=4, a(n-4) is the number of (n+5)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan Janjic, Nov 18 2007

The 5th corrector line for transforming 2^n offset 0 with a leading 1 into the fibonacci sequence. - Al Hakanson (hawkuu(AT)gmail.com), Jun 01 2009

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..23.

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].

Index entries for sequences related to Chebyshev polynomials.

FORMULA

G.f.: (1-x)/(1-2*x)^6. a(n) = 2^(n-1)*binomial(n+4, n-1)*(n+10)/n, with n>0, a(0)=1. - Wolfdieter Lang, Mar 06 2000

a(n) = 2^(n-5)*n(n+1)(n+2)(n+3)(n+9)/15. - Paul Barry, Feb 19 2003

a(n) = sum{k=0..floor((n+10)/2), C(n+10, 2k)C(k, 5) }. - Paul Barry, May 15 2003

a(n) = -A039991(n+10, 10). - N. J. A. Sloane, May 16 2003

a(n) = binomial transform of b(n)= (2*n^5 + 10*n^4 + 30*n^3 + 50*n^2 + 43*n + 15) / 15 offset 0. a(3) = 364. - Al Hakanson (hawkuu(AT)gmail.com), Jun 01 2009

a(n) = 2^(n-1)/5*Binomial(n+4,4)*(n+10). - Brad Clardy, Mar 10 2012

PROG

(MAGMA) [2^(n-1)/5*Binomial(n+4, 4)*(n+10): n in [0..25]]; // Brad Clardy, Mar 10 2012

CROSSREFS

First differences of A054849.

Sequence in context: A092044 A156149 A258402 * A260585 A084900 A300968

Adjacent sequences:  A006972 A006973 A006974 * A006976 A006977 A006978

KEYWORD

nonn,easy

AUTHOR

Simon Plouffe

STATUS

approved

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Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)