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 A054333 1/256 of tenth unsigned column of triangle A053120 (T-Chebyshev, rising powers, zeros omitted). 14
 1, 11, 65, 275, 935, 2717, 7007, 16445, 35750, 72930, 140998, 260338, 461890, 791350, 1314610, 2124694, 3350479, 5167525, 7811375, 11593725, 16921905, 24322155, 34467225, 48208875, 66615900, 91018356, 123058716, 164750740 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS If a 2-set Y and an (n-3)-set Z are disjoint subsets of an n-set X then a(n-10) is the number of 10-subsets of X intersecting both Y and Z. - Milan Janjic, Sep 08 2007 9-dimensional square numbers, eighth partial sums of binomial transform of [1,2,0,0,0,...]. a(n)=sum{i=0,n,C(n+8,i+8)*b(i)}, where b(i)=[1,2,0,0,0,...]. - Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009 2*a(n) is number of ways to place 8 queens on an (n+8) X (n+8) chessboard so that they diagonally attack each other exactly 28 times. The maximal possible attack number, p=binomial(k,2) =28 for k=8 queens, is achievable only when all queens are on the same diagonal. In graph-theory representation they thus form the corresponding complete graph. - Antal Pinter, Dec 27 2015 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. A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196. Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990. LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 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 Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1). FORMULA a(n) = (2*n+9)*binomial(n+8, 8)/9 = ((-1)^n)*A053120(2*n+9, 9)/2^8. G.f.: (1+x)/(1-x)^10. a(n) = 2*C(n+9, 9) - C(n+8, 8). - Paul Barry, Mar 04 2003 a(n) = C(n+8,8) + 2*C(n+8,9). - Borislav St. Borisov (b.st.borisov(AT)abv.bg), Mar 05 2009 E.g.f.: (1/362880)*exp(x)*(362880 + 3628800*x + 7983360*x^2 + 6773760*x^3 + 2751840*x^4 + 592704*x^5 + 70560*x^6 + 4608*x^7 + 153*x^8 + 2*x^9). - Stefano Spezia, Dec 03 2018 MATHEMATICA LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 11, 65, 275, 935, 2717, 7007, 16445, 35750, 72930}, 30] (* Vincenzo Librandi, Feb 14 2016 *) PROG (MAGMA) [Binomial(n+8, 8)+2*Binomial(n+8, 9): n in [0..40]]; // Vincenzo Librandi, Feb 14 2016 (PARI) vector(40, n, n--; (2*n+9)*binomial(n+8, 8)/9) \\ G. C. Greubel, Dec 02 2018 (Sage) [(2*n+9)*binomial(n+8, 8)/9 for n in range(40)] # G. C. Greubel, Dec 02 2018 (GAP)  List([0..30], n->(2*n+9)*Binomial(n+8, 8)/9); # Muniru A Asiru, Dec 06 2018 CROSSREFS Partial sums of A053347. Cf. A053120, A000581. Cf. A005585, A040977, A050486, A053347. - Vladimir Joseph Stephan Orlovsky, Jan 15 2009 Cf. A111125, fifth column (s=4, without leading zeros). - Wolfdieter Lang, Oct 18 2012 Sequence in context: A161459 A162288 A161776 * A267173 A266765 A036601 Adjacent sequences:  A054330 A054331 A054332 * A054334 A054335 A054336 KEYWORD nonn,easy AUTHOR Barry E. Williams, Wolfdieter Lang, Mar 15 2000 STATUS approved

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Last modified October 19 21:01 EDT 2019. Contains 328225 sequences. (Running on oeis4.)