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 A006975 Negated coefficients of Chebyshev T polynomials: a(n) = -A053120(n+10, n), n >= 0. (Formerly M4796) 11
 1, 11, 72, 364, 1568, 6048, 21504, 71808, 228096, 695552, 2050048, 5870592, 16400384, 44843008, 120324096, 317521920, 825556992, 2118057984, 5369233408, 13463453696, 33426505728, 82239815680, 200655503360, 485826232320 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A069038. - Paul Barry, Feb 19 2003 If X_1, X_2, ..., X_n are 2-blocks of a (2n+1)-set X then, for n>=4, a(n-4) is the number of (n+5)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan Janjic, Nov 18 2007 The 5th 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 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]. FORMULA G.f.: (1-x)/(1-2*x)^6. a(n) = 2^(n-1)*binomial(n+4, 4)*(n+10)/5, for n >= 0. [a(n) from Mar 06 2000 rewritten. See the Brad Clardy formula below, and a comment in A053120 on subdiagonals. - Wolfdieter Lang, Jan 03 2020] a(n) = 2^(n-4)*(n+1)(n+2)(n+3)(n+4)(n+10)/15. - Paul Barry, Feb 19 2003 a(n) = sum{k=0..floor((n+10)/2), C(n+10, 2k)C(k, 5) }. - Paul Barry, May 15 2003 a(n) = -A039991(n+10, 10). - N. J. A. Sloane, May 16 2003 a(n) = binomial transform of b(n)= (2*n^5 + 10*n^4 + 30*n^3 + 50*n^2 + 43*n + 15) / 15 offset 0. a(3) = 364. - Al Hakanson (hawkuu(AT)gmail.com), Jun 01 2009 a(n) = 2^(n-1)/5*Binomial(n+4,4)*(n+10). - Brad Clardy, Mar 10 2012 E.g.f.: (1/15)*exp(2*x)*(15+135*x+240*x^2+140*x^3+30*x^4+2*x^5). - Stefano Spezia, Jan 03 2020 PROG (MAGMA) [2^(n-1)/5*Binomial(n+4, 4)*(n+10): n in [0..25]]; // Brad Clardy, Mar 10 2012 CROSSREFS First differences of A054849. Cf. A039991, A053120, A069038. Sequence in context: A092044 A156149 A258402 * A260585 A084900 A300968 Adjacent sequences:  A006972 A006973 A006974 * A006976 A006977 A006978 KEYWORD nonn,easy AUTHOR EXTENSIONS Name clarified by Wolfdieter Lang, Nov 26 2019 STATUS approved

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Last modified January 17 02:20 EST 2021. Contains 340213 sequences. (Running on oeis4.)