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%I #15 Sep 06 2022 02:59:30
%S 1,54,945,9240,62370,324324,1387386,5096520,16563690,48668620,
%T 131405274,330142176,779502360,1743502320,3718285560,7601828256,
%U 14966099379,28482196050,52568991475,94362067800,165133618650,282337298100,472506635250,775303893000,1249100716500
%N a(n) = C(n+5,5)*C(n+8,8).
%H T. D. Noe, <a href="/A107420/b107420.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
%F From _Chai Wah Wu_, Apr 10 2021: (Start)
%F a(n) = 14*a(n-1) - 91*a(n-2) + 364*a(n-3) - 1001*a(n-4) + 2002*a(n-5) - 3003*a(n-6) + 3432*a(n-7) - 3003*a(n-8) + 2002*a(n-9) - 1001*a(n-10) + 364*a(n-11) - 91*a(n-12) + 14*a(n-13) - a(n-14) for n > 13.
%F G.f.: (56*x^5 + 350*x^4 + 560*x^3 + 280*x^2 + 40*x + 1)/(x - 1)^14. (End)
%F From _Amiram Eldar_, Sep 06 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 2200*Pi^2 - 19150081/882.
%F Sum_{n>=0} (-1)^n/a(n) = 693421/490 - 20*Pi^2 - 12288*log(2)/7. (End)
%e a(0) = C(0+5,5)*C(0+8,8) = C(5,5)*C(8,8) = 1*1 = 1.
%e a(9) = C(9+5,5)*C(9+8,8) = C(14,5)*C(17,8) = 2002*24310 = 48668620.
%t a[n_] := Binomial[n + 5, 5] * Binomial[n + 8, 8]; Array[a, 30, 0] (* _Amiram Eldar_, Sep 06 2022 *)
%o (PARI) for(n=0,29,print1(binomial(n+5,5)*binomial(n+8,8),","))
%Y Cf. A062145.
%K easy,nonn
%O 0,2
%A _Zerinvary Lajos_, May 26 2005
%E More terms from _Rick L. Shepherd_, May 27 2005
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