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 A053138 Binomial coefficients C(2*n+9,9). 4
 1, 55, 715, 5005, 24310, 92378, 293930, 817190, 2042975, 4686825, 10015005, 20160075, 38567100, 70607460, 124403620, 211915132, 350343565, 563921995, 886163135, 1362649145, 2054455634, 3042312350, 4431613550, 6358402050, 8996462475, 12565671261, 17341763505 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Even indexed members of tenth column of Pascal's triangle A007318. Number of standard tableaux of shape (2n+1,1^9). - Emeric Deutsch, May 30 2004 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 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) = binomial(2*n+9, 9) = A000582(2*n+9). G.f.: (1 + 45*x + 210*x^2 + 210*x^3 + 45*x^4 + x^5) / (1-x)^10. G.f.: (1 + x) * (x^4 + 44*x^3 + 166*x^2 + 44*x + 1) / (1-x)^10. a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n > 9. - Wesley Ivan Hurt, Dec 05 2016 MAPLE A053138:=n->binomial(2*n+9, 9): seq(A053138(n), n=0..40); # Wesley Ivan Hurt, Dec 05 2016 MATHEMATICA Table[Binomial[2n+9, 9], {n, 0, 30}] (* Harvey P. Dale, Dec 08 2011 *) PROG (MAGMA)[Binomial(2*n+9, 9): n in [0..30]]; // Vincenzo Librandi, Oct 07 2011 (PARI) for(n=0, 30, binomial(2*n+9, 9), ", ")) \\ G. C. Greubel, Sep 03 2018 CROSSREFS Cf. A000582, A007318, A053131, A053137. Sequence in context: A213341 A132155 A173377 * A027784 A297523 A221786 Adjacent sequences:  A053135 A053136 A053137 * A053139 A053140 A053141 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified September 20 10:24 EDT 2020. Contains 337264 sequences. (Running on oeis4.)