A053131 Binomial coefficients C(2*n-8,9).

10, 220, 2002, 11440, 48620, 167960, 497420, 1307504, 3124550, 6906900, 14307150, 28048800, 52451256, 94143280, 163011640, 273438880, 445891810, 708930508, 1101716330, 1677106640, 2505433700, 3679075400, 5317936260, 7575968400, 10648873950, 14783142660

Offset

9,1

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 = 9..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 Janjić, Two Enumerative Functions.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45, 10,-1).

Index entries for sequences related to Chebyshev polynomials.

Formula

a(n) = binomial(2*n-8, 9) if n >= 9 else 0.

G.f.: (10+120*x+252*x^2+120*x^3+10*x^4)/(1-x)^10.

a(n) = 2*A053133(n).

a(n) = -A053123(n,9), n >= 9; a(n) := 0, n=0..8 (tenth column of shifted Chebyshev's S-triangle, decreasing order).

From Amiram Eldar, Oct 21 2022: (Start)

Sum_{n>=9} 1/a(n) = 223611/280 - 1152*log(2).

Sum_{n>=9} (-1)^(n+1)/a(n) = 72*log(2) - 13947/280. (End)

Mathematica

Binomial[2*Range[9, 40]-8, 9] (* Harvey P. Dale, Mar 19 2012 *)

Prog

(Magma)[Binomial(2*n-8, 9): n in [9..40]]; // Vincenzo Librandi, Oct 07 2011
(PARI) for(n=9, 50, print1(binomial(2*n-8, 9), ", ")) \\ G. C. Greubel, Aug 26 2018

Crossrefs

Cf. A053123, A053130, A053133.

Sequence in context: A024291 A024292 A094420 * A334908 A166181 A199748

Adjacent sequences: A053128 A053129 A053130 * A053132 A053133 A053134

Keyword

nonn,easy

Author

Wolfdieter Lang

Status

approved