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A104674 a(n) = binomial(n+6, 6) * binomial(n+11, n).

%I A104674 #14 Mar 02 2025 08:00:55
%S A104674 1,84,2184,30576,286650,2018016,11435424,54609984,226972746,840639800,
%T A104674 2824549728,8730426432,25099975992,67725379008,172768824000,
%U A104674 419252346240,972796459635,2167754048460,4656656844840,9674494830000,19494107082450,38192536324800,72913023892800
%N A104674 a(n) = binomial(n+6, 6) * binomial(n+11, n).
%H A104674 Andrew Howroyd, <a href="/A104674/b104674.txt">Table of n, a(n) for n = 0..1000</a>
%H A104674 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).
%F A104674 From _Amiram Eldar_, Aug 30 2022: (Start)
%F A104674 Sum_{n>=0} 1/a(n) = 33033*Pi^2 - 16431490141/50400.
%F A104674 Sum_{n>=0} (-1)^n/a(n) = 1171456*log(2)/105 - 11*Pi^2/2 - 1625274871/211680. (End)
%F A104674 G.f.: (1 + 66*x + 825*x^2 + 3300*x^3 + 4950*x^4 + 2772*x^5 + 462*x^6)/(1 - x)^18. - _G. C. Greubel_, Mar 01 2025
%e A104674 If n=0 then C(0+6,6)*C(0+11,0+0) = C(6,6)*C(11,0) = 1*1 = 1.
%e A104674 If n=8 then C(8+6,6)*C(8+11,8+0) = C(14,6)*C(19,8) = 3003*75582 = 226972746.
%t A104674 a[n_] := Binomial[n + 6, 6] * Binomial[n + 11, n]; Array[a, 25, 0] (* _Amiram Eldar_, Aug 30 2022 *)
%o A104674 (PARI) a(n)={binomial(n+6, 6) * binomial(n+11, n)} \\ _Andrew Howroyd_, Nov 08 2019
%o A104674 (Magma)
%o A104674 A104674:= func< n | Binomial(n+6,n)*Binomial(n+11,n) >;
%o A104674 [A104674(n): n in [0..30]]; // _G. C. Greubel_, Mar 01 2025
%o A104674 (SageMath)
%o A104674 def A104674(n): return binomial(n+6,n)*binomial(n+11,n)
%o A104674 print([A104674(n) for n in range(31)]) # _G. C. Greubel_, Mar 01 2025
%Y A104674 Cf. A062190.
%K A104674 easy,nonn
%O A104674 0,2
%A A104674 _Zerinvary Lajos_, Apr 22 2005
%E A104674 a(8) corrected and terms a(9) and beyond from _Andrew Howroyd_, Nov 08 2019