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A006974
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Coefficients of Chebyshev T polynomials: a(n) = A053120(n+8, n), n >= 0.
(Formerly M4631)
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14
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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
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OFFSET
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0,2
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COMMENTS
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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 Janjic, Nov 18 2007
The fourth 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]
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REFERENCES
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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).
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LINKS
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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].
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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, 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. [Al Hakanson (hawkuu(AT)gmail.com), Jun 01 2009]
E.g.f.: (1/3)*exp(2*x)*(3 + 21*x + 27*x^2 + 10*x^3 + x^4). - Stefano Spezia, Aug 17 2019
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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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PROG
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(Magma) [2^(n-1)/4*Binomial(n+3, 3)*(n+8) : n in [0..25]]; // Brad Clardy, Mar 08 2012
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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