A006974 Coefficients of Chebyshev T polynomials: a(n) = A053120(n+8, n), n >= 0.
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
Offset: 0
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
- 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
- M. H. Albert, M. D. Atkinson, R. Brignall, The enumeration of three pattern classes using monotone grid classes, El. J. Combinat. 19 (3) (2012) P20, Chapter 5.4.1.
- Index entries for sequences related to Chebyshev polynomials.
Programs
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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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Maple
a := n->n*(n+1)*(n+2)*(n+7)*2^(n-5)/3;
Formula
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]
a(n) = 2^(n-3)*binomial(n+3, 3)*(n+8). - Brad Clardy, Mar 08 2012 [See a comment in A053120 on subdiagonals. - Wolfdieter Lang, Jan 03 2020]
E.g.f.: (1/3)*exp(2*x)*(3 + 21*x + 27*x^2 + 10*x^3 + x^4). - Stefano Spezia, Aug 17 2019
Extensions
Name clarified by Wolfdieter Lang, Nov 26 2019
Comments