A107397 a(n) = binomial(n+6, 6) * binomial(n+8, 6).
28, 588, 5880, 38808, 194040, 792792, 2774772, 8588580, 24048024, 61941880, 148660512, 335785632, 719540640, 1472290848, 2891999880, 5477788008, 10042611348, 17877713700, 30988037080, 52423371000, 86736850200, 140610670200, 223698793500, 349748200620, 538074154800
Offset: 0
Examples
If n=0 then C(0+6,6)*C(0+8,6) = C(6,6)*C(8,6) = 1*28 = 28. If n=6 then C(6+6,6)*C(6+8,6) = C(12,6)*C(14,6) = 924*3003 = 2774772.
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
Programs
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Magma
A107397:= func< n | Binomial(n+6,6)*Binomial(n+8,6) >; [A107397(n): n in [0..30]]; // G. C. Greubel, Feb 09 2025
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Mathematica
a[n_] := Binomial[n + 6, 6] * Binomial[n + 8, 6]; Array[a, 25, 0] (* Amiram Eldar, Sep 01 2022 *)
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PARI
a(n)={binomial(n+6, 6) * binomial(n+8, 6)} \\ Andrew Howroyd, Nov 08 2019 -
SageMath
def A107397(n): return binomial(n+6,6)*binomial(n+8,6) print([A107397(n) for n in range(31)]) # G. C. Greubel, Feb 09 2025
Formula
From Amiram Eldar, Sep 01 2022: (Start)
Sum_{n>=0} 1/a(n) = 720*Pi^2 - 1740989/245.
Sum_{n>=0} (-1)^n/a(n) = 6144*log(2)/7 - 149046/245. (End)
G.f.: 28*(1 + 8*x + 15*x^2 + 8*x^3 + x^4)/(1-x)^13. - G. C. Greubel, Feb 09 2025
Extensions
a(3) corrected and terms a(11) and beyond from Andrew Howroyd, Nov 08 2019