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

Author

Wolfdieter Lang

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A053123, A053129.

Programs

Magma

[Binomial(2*n-7, 8): n in [8..50]]; // Vincenzo Librandi, Apr 07 2011

Mathematica

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

PARI

for(n=8,50, print1(binomial(2*n-7,8), ", ")) \\ G. C. Greubel, Aug 26 2018

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)