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A053131 Binomial coefficients C(2*n-8,9). 6
10, 220, 2002, 11440, 48620, 167960, 497420, 1307504, 3124550, 6906900, 14307150, 28048800, 52451256, 94143280, 163011640, 273438880, 445891810, 708930508, 1101716330, 1677106640, 2505433700, 3679075400, 5317936260 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,1

COMMENTS

a(n) = -A053123(n,9), n >= 9; a(n) := 0, n=0..8 (tenth 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 = 9..200

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].

Index entries for sequences related to Chebyshev polynomials.

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-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).

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 * A166181 A199748 A210137

Adjacent sequences:  A053128 A053129 A053130 * A053132 A053133 A053134

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified November 17 13:33 EST 2019. Contains 329230 sequences. (Running on oeis4.)