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%I #18 Sep 06 2022 03:00:44
%S 1,24,210,1120,4410,14112,38808,95040,212355,440440,858858,1589952,
%T 2815540,4798080,7907040,12651264,19718181,30020760,44753170,65456160,
%U 94093230,133138720,185679000,255528000,347358375,466849656,620854794,817586560,1066825320
%N a(n) = C(n+5,n)*C(n+3,3).
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F G.f.: -(10*x^3+30*x^2+15*x+1) / (x-1)^9. - _Colin Barker_, Jan 28 2013
%F From _Amiram Eldar_, Sep 06 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 75*Pi^2/2 - 5905/16.
%F Sum_{n>=0} (-1)^n/a(n) = 160*log(2) - 5*Pi^2/4 - 4685/48. (End)
%e If n=0 then C(0+5,0)*C(0+3,3) = C(5,0)*C(3,3) = 1*1 = 1.
%e If n=15 then C(15+5,15)*C(15+3,3) = C(20,15)*C(18,3) = 15504*816 = 12651264.
%p A105946:=n->binomial(n+5,n)*binomial(n+3,3); seq(A105946(n), n=0..100); # _Wesley Ivan Hurt_, Nov 26 2013
%t Table[Binomial[n+5,n]*Binomial[n+3,3], {n,0,100}] (* _Wesley Ivan Hurt_, Nov 26 2013 *)
%t LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,24,210,1120,4410,14112,38808,95040,212355},110] (* _Harvey P. Dale_, Jun 28 2015 *)
%Y Cf. A062196.
%K easy,nonn
%O 0,2
%A _Zerinvary Lajos_, Apr 27 2005
%E More terms from _Colin Barker_, Jan 28 2013
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