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 A006974 Coefficients of Chebyshev T polynomials: a(n) = A053120(n+8, n), n >= 0. (Formerly M4631) 14
 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; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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] 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. 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-1)/4*Binomial(n+3,3)*(n+8). - Brad Clardy, Mar 08 2012 E.g.f.: (1/3)*exp(2*x)*(3 + 21*x + 27*x^2 + 10*x^3 + x^4). - Stefano Spezia, Aug 17 2019 MAPLE a := n->n*(n+1)*(n+2)*(n+7)*2^(n-5)/3; PROG (MAGMA) [2^(n-1)/4*Binomial(n+3, 3)*(n+8) : n in [0..25]]; // Brad Clardy, Mar 08 2012 CROSSREFS Cf. A039991 (see column 8), A003472 (partial sums), A053120. Sequence in context: A116169 A280549 A084367 * A279979 A222993 A171480 Adjacent sequences:  A006971 A006972 A006973 * A006975 A006976 A006977 KEYWORD nonn,easy AUTHOR EXTENSIONS Name clarified by Wolfdieter Lang, Nov 26 2019 STATUS approved

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Last modified December 12 17:50 EST 2019. Contains 329960 sequences. (Running on oeis4.)