A053133 One half of binomial coefficients binomial(2*n-8,9).

5, 110, 1001, 5720, 24310, 83980, 248710, 653752, 1562275, 3453450, 7153575, 14024400, 26225628, 47071640, 81505820, 136719440, 222945905, 354465254, 550858165, 838553320, 1252716850, 1839537700, 2658968130, 3787984200, 5324436975, 7391571330, 10143295635

Offset

9,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 9..200

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)/2.

G.f.: (5+60*x+126*x^2+60*x^3+5*x^4)/(1-x)^10.

a(n) = A053131(n)/2.

From Amiram Eldar, Nov 03 2022: (Start)

Sum_{n>=9} 1/a(n) = 223611/140 - 2304*log(2).

Sum_{n>=9} (-1)^(n+1)/a(n) = 144*log(2) - 13947/140. (End)

Mathematica

Table[Binomial[2*n-8, 9]/2, {n, 9, 50}] (* G. C. Greubel, Aug 26 2018 *)

Prog

(PARI) a(n)=binomial(2*n-8, 9)/2 \\ Charles R Greathouse IV, Oct 03 2011
(Magma) [Binomial(2*n-8, 9)/2: n in [9..40]]; // Vincenzo Librandi, Oct 07 2011

Crossrefs

Cf. A053131.

Sequence in context: A281762 A265082 A215786 * A203367 A322631 A294965

Adjacent sequences: A053130 A053131 A053132 * A053134 A053135 A053136

Keyword

nonn,easy

Author

Wolfdieter Lang

Status

approved