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a(n) = C(n+8,n)*C(n+11,8).
0

%I #12 Sep 08 2022 08:14:59

%S 165,4455,57915,495495,3185325,16563690,73002930,281582730,972740340,

%T 3062330700,8904315420,24168856140,61764854580,149660993790,

%U 345855237750,766005304350,1632800780325,3361648665375,6705510829875,12993932469375,24518985616125

%N a(n) = C(n+8,n)*C(n+11,8).

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

%F G.f.: -165*(x+1)*(x^4+9*x^3+19*x^2+9*x+1) / (x-1)^17. - _Colin Barker_, Jan 28 2013

%F From _Amiram Eldar_, Sep 08 2022: (Start)

%F Sum_{n>=0} 1/a(n) = 1493776559/14175 - 32032*Pi^2/3.

%F Sum_{n>=0} (-1)^n/a(n) = 112*Pi^2 - 1740989/1575. (End)

%e If n=0 then C(0+8,0)*C(0+11,8) = C(8,0)*C(11,8) = 1*165 = 165.

%e If n=4 then C(4+8,4)*C(4+11,8) = C(12,4)*C(15,8) = 495*6435 = 3185325.

%t Table[Binomial[n+8,n]Binomial[n+11,8],{n,0,30}] (* _Harvey P. Dale_, Apr 26 2018 *)

%Y Cf. A062145.

%K easy,nonn

%O 0,1

%A _Zerinvary Lajos_, Apr 27 2005

%E More terms from _Colin Barker_, Jan 28 2013