cp's OEIS Frontend

A105948 a(n) = C(n+5,5) * C(n+7,7).

%I A105948 #24 Feb 22 2025 04:02:45
%S A105948 1,48,756,6720,41580,199584,792792,2718144,8281845,22902880,58402344,
%T A105948 139007232,311800944,664191360,1352103840,2644114176,4988699793,
%U A105948 9114302736,16175074300,27959131200,47181033900,77886151200,126001769400,200078424000,312275179125
%N A105948 a(n) = C(n+5,5) * C(n+7,7).
%H A105948 T. D. Noe, <a href="/A105948/b105948.txt">Table of n, a(n) for n = 0..1000</a>
%H A105948 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A105948 G.f.: (1 + 35*x + 210*x^2 + 350*x^3 + 175*x^4 + 21*x^5)/ (1-x)^13. - _Colin Barker_, Jan 29 2013
%F A105948 From _Amiram Eldar_, Sep 06 2022: (Start)
%F A105948 Sum_{n>=0} 1/a(n) = 1225*Pi^2 - 1740851/144.
%F A105948 Sum_{n>=0} (-1)^n/a(n) = 35*Pi^2/6 - 3584*log(2)/3 + 61719/80. (End)
%e A105948 If n=0 then C(0+7,0)*C(0+5,5) = C(7,0)*C(5,5) = 1*1 = 1.
%e A105948 If n=12 then C(12+7,12)*C(12+5,5) = C(19,12)*C(17,5) = 50388*6188 = 311800944.
%t A105948 Table[Binomial[n+7,n]Binomial[n+5,5],{n,0,30}] (* _Harvey P. Dale_, Apr 08 2019 *)
%o A105948 (Magma)
%o A105948 A105948:= func< n | Binomial(n+5,5)*Binomial(n+7,7) >;
%o A105948 [A105948(n): n in [0..40]]; // _G. C. Greubel_, Feb 22 2025
%o A105948 (SageMath)
%o A105948 def A105948(n): return binomial(n+5,5)*binomial(n+7,7)
%o A105948 print([A105948(n) for n in range(41)]) # _G. C. Greubel_, Feb 22 2025
%Y A105948 Cf. A062196.
%K A105948 easy,nonn
%O A105948 0,2
%A A105948 _Zerinvary Lajos_, Apr 27 2005