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A107421 a(n) = binomial(n+6,6)*binomial(n+9,9).

%I A107421 #16 Mar 10 2025 05:07:38
%S A107421 1,70,1540,18480,150150,924924,4624620,19631040,73002930,243343100,
%T A107421 739763024,2078672960,5456516520,13495999440,31674284400,70950397056,
%U A107421 152432493675,315413948850,630827897700,1223211990000,2305754601150,4235059471500,7595106655500
%N A107421 a(n) = binomial(n+6,6)*binomial(n+9,9).
%H A107421 T. D. Noe, <a href="/A107421/b107421.txt">Table of n, a(n) for n = 0..1000</a>
%H A107421 <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 A107421 G.f.: (1+54*x+540*x^2+1680*x^3+1890*x^4+756*x^5+84*x^6)/(1-x)^16. - _Harvey P. Dale_, Jan 30 2013
%F A107421 From _Amiram Eldar_, Sep 06 2022: (Start)
%F A107421 Sum_{n>=0} 1/a(n) = 11583*Pi^2 - 4481289621/39200.
%F A107421 Sum_{n>=0} (-1)^n/a(n) = 73728*log(2)/35 - 225*Pi^2/2 - 13673259/39200. (End)
%e A107421 If n=0 then C(0+6,6)*C(0+9,9) = C(6,6)*C(9,9) = 1*1 = 1.
%e A107421 If n=7 then C(7+6,6)*C(7+9,9) = C(13,6)*C(16,9) = 1716*11440 = 19631040.
%t A107421 Table[Binomial[n+6,6]Binomial[n+9,9],{n,0,30}] (* _Harvey P. Dale_, Jan 30 2013 *)
%o A107421 (PARI) for(n=0,29,print1(binomial(n+6,6)*binomial(n+9,9),","))
%o A107421 (Magma)
%o A107421 A107421:= func< n | Binomial(n+6,n)*Binomial(n+9,n) >;
%o A107421 [A107421(n): n in [0..40]]; // _G. C. Greubel_, Mar 09 2025
%o A107421 (SageMath)
%o A107421 def A107421(n): return binomial(n+6,n)*binomial(n+9,n)
%o A107421 print([A107421(n) for n in range(41)]) # _G. C. Greubel_, Mar 09 2025
%Y A107421 Cf. A062145.
%K A107421 easy,nonn
%O A107421 0,2
%A A107421 _Zerinvary Lajos_, May 26 2005
%E A107421 Corrected and extended by _Rick L. Shepherd_, May 27 2005