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%I #18 Sep 06 2022 03:00:57
%S 1,48,756,6720,41580,199584,792792,2718144,8281845,22902880,58402344,
%T 139007232,311800944,664191360,1352103840,2644114176,4988699793,
%U 9114302736,16175074300,27959131200,47181033900,77886151200,126001769400,200078424000,312275179125
%N a(n) = C(n+7,n)*C(n+5,5).
%H T. D. Noe, <a href="/A105948/b105948.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F G.f.: -(21*x^5+175*x^4+350*x^3+210*x^2+35*x+1) / (x-1)^13. - _Colin Barker_, Jan 29 2013
%F From _Amiram Eldar_, Sep 06 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 1225*Pi^2 - 1740851/144.
%F Sum_{n>=0} (-1)^n/a(n) = 35*Pi^2/6 - 3584*log(2)/3 + 61719/80. (End)
%e If n=0 then C(0+7,0)*C(0+5,5) = C(7,0)*C(5,5) = 1*1 = 1.
%e If n=12 then C(12+7,12)*C(12+5,5) = C(19,12)*C(17,5) = 50388*6188 = 311800944.
%t Table[Binomial[n+7,n]Binomial[n+5,5],{n,0,30}] (* or *) LinearRecurrence[ {13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{1,48,756,6720,41580,199584,792792,2718144,8281845,22902880,58402344,139007232,311800944},30] (* _Harvey P. Dale_, Apr 08 2019 *)
%Y Cf. A062196.
%K easy,nonn
%O 0,2
%A _Zerinvary Lajos_, Apr 27 2005
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