A053130 Binomial coefficients C(2*n-7,8).

9, 165, 1287, 6435, 24310, 75582, 203490, 490314, 1081575, 2220075, 4292145, 7888725, 13884156, 23535820, 38608020, 61523748, 95548245, 145008513, 215553195, 314457495, 450978066, 636763050, 886322710, 1217566350, 1652411475, 2217471399, 2944827765, 3872894697

Offset

8,1

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 = 8..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 (9,-36,84,-126,126,-84,36,-9,1).

Index entries for sequences related to Chebyshev polynomials.

Formula

a(n) = binomial(2*n-7, 8) if n >= 8 else 0.

G.f.: (9+84*x+126*x^2+36*x^3+x^4)/(1-x)^9.

a(n) = A053123(n,8), n >= 8; a(n) := 0, n=0..7, (ninth column of shifted Chebyshev's S-triangle, decreasing order).

From Amiram Eldar, Oct 21 2022: (Start)

Sum_{n>=8} 1/a(n) = 37276/105 - 512*log(2).

Sum_{n>=8} (-1)^n/a(n) = 592/21 - 16*Pi + 32*log(2). (End)

Mathematica

Table[Binomial[2*n-7, 8], {n, 8, 50}] (* G. C. Greubel, Aug 26 2018 *)

Prog

(Magma) [Binomial(2*n-7, 8): n in [8..50]]; // Vincenzo Librandi, Apr 07 2011
(PARI) for(n=8, 50, print1(binomial(2*n-7, 8), ", ")) \\ G. C. Greubel, Aug 26 2018

Crossrefs

Cf. A053123, A053129.

Sequence in context: A354900 A354892 A086759 * A219074 A166180 A004107

Adjacent sequences: A053127 A053128 A053129 * A053131 A053132 A053133

Keyword

nonn,easy

Author

Wolfdieter Lang

Status

approved