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A104478 a(n) = binomial(n+8,8)*binomial(n+12,8).

%I A104478 #36 Mar 05 2025 10:46:28
%S A104478 495,11583,135135,1061775,6370650,31286970,131405274,486370170,
%T A104478 1621233900,4946841900,13992495660,37058912748,92647281870,
%U A104478 220089696750,499568676750,1088533853550,2285921092455,4642276728375,9143878404375,17513561154375,32691980821500,59592810754620
%N A104478 a(n) = binomial(n+8,8)*binomial(n+12,8).
%C A104478 All terms are multiples of 99. - _Michel Marcus_, Aug 01 2015
%H A104478 G. C. Greubel, <a href="/A104478/b104478.txt">Table of n, a(n) for n = 0..1000</a>
%H A104478 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
%F A104478 a(n) = A000581(n+8)*A000581(n+12). - _Michel Marcus_, Aug 01 2015
%F A104478 From _Amiram Eldar_, Sep 04 2022: (Start)
%F A104478 Sum_{n>=0} 1/a(n) = 11648*Pi^2/3 - 65726161036/1715175.
%F A104478 Sum_{n>=0} (-1)^n/a(n) = 262144*log(2)/99 - 629604992/343035. (End)
%F A104478 G.f.: 99*(5 + 32*x + 56*x^2 + 32*x^3 + 5*x^4)/(1-x)^17. - _G. C. Greubel_, Mar 04 2025
%e A104478 a(0): C(0+8,8)*C(0+12,8) = C(8,8)*C(12,8) = 1*495 = 495.
%e A104478 a(7): C(7+8,8)*C(7+12,8) = C(15,8)*C(19,8) = 6435*75582 = 486370170.
%t A104478 f[n_] := Binomial[n + 8, 8] * Binomial[n + 12, 8]; Table[ f[n], {n, 0, 18}] (* _Robert G. Wilson v_, Apr 19 2005 *)
%o A104478 (PARI) vector(30, n, n--; binomial(n+8,8)*binomial(n+12,8)) \\ _Michel Marcus_, Jul 31 2015
%o A104478 (Magma) [Binomial(n+8,8)*Binomial(n+12,8): n in [0..30]]; // _Vincenzo Librandi_, Jul 31 2015
%o A104478 (SageMath)
%o A104478 def A104478(n): return binomial(n+8,8)*binomial(n+12,8)
%o A104478 print([A104478(n) for n in range(31)]) # _G. C. Greubel_, Mar 04 2025
%Y A104478 Cf. A000581, A062264.
%K A104478 easy,nonn
%O A104478 0,1
%A A104478 _Zerinvary Lajos_, Apr 18 2005
%E A104478 Corrected and extended by _Robert G. Wilson v_, Apr 19 2005
%E A104478 a(6) corrected by _Georg Fischer_, May 08 2021