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A001794
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Coefficients of Chebyshev polynomials.
(Formerly M4405 N1859)
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10
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1, 7, 32, 120, 400, 1232, 3584, 9984, 26880, 70400, 180224, 452608, 1118208, 2723840, 6553600, 15597568, 36765696, 85917696, 199229440, 458752000, 1049624576, 2387607552, 5402263552, 12163481600, 27262976000, 60850962432
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| If X_1,X_2,...,X_n are 2-blocks of a (2n+1)-set X then a(n-2) is the number of (n+3)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Nov 18 2007
The third corrector line for transforming 2^n offset 0 with a leading 1 into the fibonacci sequence. [From Al Hakanson (hawkuu(AT)gmail.com), Jun 01 2009]
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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. 795.
Jones, C. W.; Miller, J. C. P.; Conn, J. F. C.; Pankhurst, R. C.; Tables of Chebyshev polynomials. Proc. Roy. Soc. Edinburgh. Sect. A. 62, (1946). 187-203.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..500
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
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.
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n) = 2^(n-2)*(n+1)*(n+2)*(n+6)/3.
G.f.: (1-x)/(1-2*x)^4.
a(n)=sum{k=0..floor((n+6)/2), C(n+6, 2*k)*C(k, 3) } - Paul Barry, May 15 2003
With a leading zero, the binomial transform of A000330. - Paul Barry, Jul 19 2003
Sum{i=0..j, sum{k=0..i, k^2}*binomial(j, i)}. - Jon Perry, Feb 26 2004
Binomial transform of a(n)=(2*n^3+6*n^2+7*n+3)/3 offset 0. a(3)=120. [From Al Hakanson (hawkuu(AT)gmail.com), Jun 01 2009]
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MAPLE
| A001794:=-(-1+z)/(2*z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
| a(n)= -A039991(n+6, 6).
Sequence in context: A190096 A164270 A182820 * A140289 A133107 A178851
Adjacent sequences: A001791 A001792 A001793 * A001795 A001796 A001797
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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 Joe Keane (jgk(AT)jgk.org), Nov 24 2001
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