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a(n) = C(n+5,5)*C(n+10,n+0).
2

%I #13 Sep 06 2022 00:57:04

%S 1,66,1386,16016,126126,756756,3699696,15402816,56316546,184940756,

%T 554822268,1540663488,4001445448,9802357488,22805484768,50678855040,

%U 108088495515,222161129190,441579528390,851355545040,1596291646950,2917485413700,5208073135200

%N a(n) = C(n+5,5)*C(n+10,n+0).

%H T. D. Noe, <a href="/A104673/b104673.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

%F G.f.: (252*x^5+1050*x^4+1200*x^3+450*x^2+50*x+1)/(x-1)^16. - _Harvey P. Dale_, Nov 24 2011

%F From _Amiram Eldar_, Aug 30 2022: (Start)

%F Sum_{n>=0} 1/a(n) = 17875*Pi^2/3 - 7468753315/127008.

%F Sum_{n>=0} (-1)^n/a(n) = 208828891/127008 - 725*Pi^2/6 - 40960*log(2)/63. (End)

%e If n=0 then C(0+5,5)*C(0+10,0+0)= C(5,5)*C(10,0)=1*1=1

%e If n=6 then C(6+5,5)*C(6+10,6+0)= C(11,5)*C(16,6)=462*8008=3699696

%t Table[Binomial[n+5,5]Binomial[n+10,n],{n,0,30}]

%Y Cf. A062190.

%K easy,nonn

%O 0,2

%A _Zerinvary Lajos_, Apr 22 2005

%E Corrected and extended by Harvey P. Dale, Nov 24 2011