cp's OEIS Frontend

A104476 a(n) = binomial(n+7,7)*binomial(n+11,7).

%I A104476 #26 Mar 05 2025 01:53:58
%S A104476 330,6336,61776,411840,2123550,9060480,33372768,109219968,324246780,
%T A104476 886828800,2261413440,5427392256,12352970916,26829982080,55895796000,
%U A104476 112183843200,217706770710,409800980160,750266946000,1339149240000,2335141487250,3985308138240
%N A104476 a(n) = binomial(n+7,7)*binomial(n+11,7).
%H A104476 T. D. Noe, <a href="/A104476/b104476.txt">Table of n, a(n) for n = 0..1000</a>
%H A104476 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F A104476 From _Amiram Eldar_, Sep 01 2022: (Start)
%F A104476 Sum_{n>=0} 1/a(n) = 539*Pi^2 - 114905813/21600.
%F A104476 Sum_{n>=0} (-1)^n/a(n) = 1741019/7200 - 49*Pi^2/2. (End)
%F A104476 G.f.: 66*(5 + 21*x + 21*x^2 + 5*x^3)/(1-x)^15. - _G. C. Greubel_, Mar 04 2025
%e A104476 a(0): C(0+7,7)*C(0+11,7) = C(7,7)*C(11,7) = 1*330 = 330;
%e A104476 a(7): C(7+7,7)*C(7+11,7) = C(14,7)*C(18,7) = 3432*31824 = 109219968.
%t A104476 f[n_] := Binomial[n + 7, 7]*Binomial[n + 11, 7]; Table[ f[n], {n, 0, 19}] (* _Robert G. Wilson v_, Apr 20 2005 *)
%o A104476 (PARI) vector(30, n, n--; binomial(n+7,7)*binomial(n+11,7)) \\ _Michel Marcus_, Jul 31 2015
%o A104476 (Magma) [Binomial(n+7,7)*Binomial(n+11,7): n in [0..30]]; // _Vincenzo Librandi_, Jul 31 2015
%o A104476 (Python)
%o A104476 A104476_list, m = [], [3432, -1716, 660, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330]
%o A104476 for _ in range(10**2):
%o A104476     A104476_list.append(m[-1])
%o A104476     for i in range(14):
%o A104476         m[i+1] += m[i] # _Chai Wah Wu_, Dec 15 2015
%o A104476 (SageMath)
%o A104476 def A104476(n): return binomial(n+7,7)*binomial(n+11,7)
%o A104476 print([A104476(n) for n in range(31)]) # _G. C. Greubel_, Mar 04 2025
%Y A104476 Cf. A062264.
%K A104476 easy,nonn
%O A104476 0,1
%A A104476 _Zerinvary Lajos_, Apr 18 2005
%E A104476 More terms from _Robert G. Wilson v_, Apr 20 2005