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Search: id:A006974
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| A006974 |
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Coefficients of Chebyshev polynomials.
(Formerly M4631)
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+0
6
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| 1, 9, 50, 220, 840, 2912, 9408, 28800, 84480, 239360, 658944, 1770496, 4659200, 12042240, 30638080, 76873728, 190513152, 466944000, 1133117440, 2724986880, 6499598336, 15386804224, 36175872000, 84515225600, 196293427200, 453437816832
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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If X_1,X_2,...,X_n are 2-blocks of a (2n+1)-set X then, for n>=3, a(n-3) is the number of (n+4)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Nov 18 2007
The fourth 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
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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LINKS
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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.
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FORMULA
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G.f.: (1-x)/(1-2*x)^5.
a(n)=sum{k=0..floor((n+8)/2), C(n+8, 2k)C(k, 4) } - Paul Barry (pbarry(AT)wit.ie), May 15 2003
Binomial transform of a(n)=(24*n^4-134*n^3+261*n^2-130*n+3)/3 offset 0. a(3)=220. [From Al Hakanson (hawkuu(AT)gmail.com), Jun 01 2009]
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MAPLE
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a := n->n*(n+1)*(n+2)*(n+7)*2^(n-5)/3;
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CROSSREFS
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a(n)= A039991(n+8, 8).
Sequence in context: A080812 A116169 A084367 this_sequence A007681 A115366 A002462
Adjacent sequences: A006971 A006972 A006973 this_sequence A006975 A006976 A006977
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KEYWORD
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nonn,easy
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com)
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