A105944 a(n) = binomial(n+8,n)*binomial(n+11,8).
165, 4455, 57915, 495495, 3185325, 16563690, 73002930, 281582730, 972740340, 3062330700, 8904315420, 24168856140, 61764854580, 149660993790, 345855237750, 766005304350, 1632800780325, 3361648665375, 6705510829875, 12993932469375, 24518985616125
Offset: 0
Examples
If n=0 then C(0+8,0)*C(0+11,8) = C(8,0)*C(11,8) = 1*165 = 165. If n=4 then C(4+8,4)*C(4+11,8) = C(12,4)*C(15,8) = 495*6435 = 3185325.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
Programs
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Magma
A105944:= func< n | Binomial(n+8,8)*Binomial(n+11,8) >; [A105944(n): n in [0..40]]; // G. C. Greubel, Mar 10 2025
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Mathematica
Table[Binomial[n+8,n]Binomial[n+11,8],{n,0,30}] (* Harvey P. Dale, Apr 26 2018 *) -
SageMath
def A105994(n): return binomial(n+8,8)*binomial(n+11,8) print([A105994(n) for n in range(41)]) # G. C. Greubel, Mar 10 2025
Formula
G.f.: 165*(1+x)*(1+9*x+19*x^2+9*x^3+x^4)/(1-x)^17. - Colin Barker, Jan 28 2013
From Amiram Eldar, Sep 08 2022: (Start)
Sum_{n>=0} 1/a(n) = 1493776559/14175 - 32032*Pi^2/3.
Sum_{n>=0} (-1)^n/a(n) = 112*Pi^2 - 1740989/1575. (End)
a(n) = 165*A030648(n). - G. C. Greubel, Mar 10 2025
Extensions
More terms from Colin Barker, Jan 28 2013