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A104670 a(n) = binomial(n+2, 2)*binomial(n+7, n).

%I A104670 #30 Mar 02 2025 08:01:03
%S A104670 1,24,216,1200,4950,16632,48048,123552,289575,629200,1283568,2482272,
%T A104670 4585308,8139600,13953600,23193984,37509021,59183784,91333000,
%U A104670 138138000,205134930,299562120,430775280,610740000,854611875,1181415456,1614834144,2184124096,2925166200
%N A104670 a(n) = binomial(n+2, 2)*binomial(n+7, n).
%H A104670 G. C. Greubel, <a href="/A104670/b104670.txt">Table of n, a(n) for n = 0..1000</a>
%H A104670 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A104670 G.f.: (1 + 14*x + 21*x^2)/(1-x)^10. - _Colin Barker_, Mar 18 2012
%F A104670 From _Amiram Eldar_, Aug 30 2022: (Start)
%F A104670 Sum_{n>=0} 1/a(n) = 49*Pi^2/3 - 288281/1800.
%F A104670 Sum_{n>=0} (-1)^n/a(n) = 448*log(2)/3 - 35*Pi^2/6 - 1799/40. (End)
%e A104670 If n=0 then C(2+0,2)*C(7+0,0+0) = C(2,2)*C(7,0) = 1*1 = 1;
%e A104670 if n=6 then C(2+6,2)*C(7+6,0+6) = C(8,2)*C(13,6) = 28*1716 = 48048.
%p A104670 [seq(stirling2(n+1,n)*binomial(n+6,7),n=1..25)]; # _Zerinvary Lajos_, Dec 06 2006
%t A104670 a[n_] := Binomial[n + 2, 2] * Binomial[n + 7, 7]; Array[a, 25, 0] (* _Amiram Eldar_, Aug 30 2022 *)
%o A104670 (Magma)
%o A104670 A104670:= func< n | Binomial(n+2,n)*Binomial(n+7,n) >;
%o A104670 [A104670(n): n in [0..30]]; // _G. C. Greubel_, Mar 01 2025
%o A104670 (SageMath)
%o A104670 def A104670(n): return binomial(n+2,n)*binomial(n+7,n)
%o A104670 print([A104670(n) for n in range(31)]) # _G. C. Greubel_, Mar 01 2025
%Y A104670 Cf. A000217, A000580, A062190.
%K A104670 easy,nonn
%O A104670 0,2
%A A104670 _Zerinvary Lajos_, Apr 22 2005
%E A104670 Corrected and extended by _Don Reble_, Nov 21 2006