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 A053128 Binomial coefficients C(2*n-5,6). 6
 7, 84, 462, 1716, 5005, 12376, 27132, 54264, 100947, 177100, 296010, 475020, 736281, 1107568, 1623160, 2324784, 3262623, 4496388, 6096454, 8145060, 10737573, 13983816, 18009460, 22957480, 28989675, 36288252, 45057474, 55525372, 67945521, 82598880, 99795696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,1 COMMENTS a(n) = A053123(n,6), n >= 6; a(n) = 0, n=0..5, (seventh column of shifted Chebyshev's S-triangle, decreasing order). REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings). LINKS Vincenzo Librandi, Table of n, a(n) for n = 6..200 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, University of Banja Luka (Bosnia and Herzegovina, 2017). Ângela Mestre, José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4. Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA a(n) = binomial(2*n-5, 6) if n >= 6 else 0. G.f.: (7+35*x+21*x^2+x^3)/(1-x)^7. E.g.f.: (18900 - 16380*x + 6975*x^2 - 1935*x^3 + 390*x^4 - 60*x^5 + 8*x^6)*exp(x)/90. - G. C. Greubel, Aug 26 2018 a(n) = (n-5)*(n-4)*(n-3)*(2*n-9)*(2*n-7)*(2*n-5)/90. - Wesley Ivan Hurt, Mar 25 2020 MATHEMATICA Table[Binomial[2*n-5, 6], {n, 6, 50}] (* G. C. Greubel, Aug 26 2018 *) PROG (MAGMA) [Binomial(2*n-5, 6): n in [6..40]]; // Vincenzo Librandi, Oct 07 2011 (PARI) for(n=6, 50, print1(binomial(2*n-5, 6), ", ")) \\ G. C. Greubel, Aug 26 2018 CROSSREFS Cf. A053123, A053127. Sequence in context: A231259 A187649 A316377 * A027819 A269895 A272496 Adjacent sequences:  A053125 A053126 A053127 * A053129 A053130 A053131 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 16 19:46 EDT 2021. Contains 343951 sequences. (Running on oeis4.)