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A004334 Binomial coefficient C(4n,n-4).

%I A004334 #38 Apr 25 2025 14:39:44
%S A004334 1,20,276,3276,35960,376992,3838380,38320568,377348994,3679075400,
%T A004334 35607051480,342700125300,3284214703056,31368725759168,
%U A004334 298824321028320,2840671544105280,26958221130508525,255485622301674660
%N A004334 Binomial coefficient C(4n,n-4).
%D A004334 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
%H A004334 Vincenzo Librandi, <a href="/A004334/b004334.txt">Table of n, a(n) for n = 4..1000</a>
%H A004334 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A004334 Daniel W. Stasiuk, <a href="http://hdl.handle.net/10388/11865">An Enumeration Problem for Sequences of n-ary Trees Arising from Algebraic Operads</a>, Master's Thesis, University of Saskatchewan-Saskatoon (2018).
%F A004334 From _Ilya Gutkovskiy_, Jan 31 2017: (Start)
%F A004334 E.g.f.: (1/24)*x^4*3F3(17/4,9/2,19/4; 17/3,6,19/3; 256*x/27).
%F A004334 a(n) ~ 2^(8*n+1/2)/(sqrt(Pi*n)*3^(3*n+9/2)). (End)
%F A004334 D-finite with recurrence -3*(3*n+2)*(n-4)*(3*n+4)*(n+1)*a(n) +8*n*(4*n-3)*(2*n-1)*(4*n-1)*a(n-1)=0. - _R. J. Mathar_, Mar 19 2025
%t A004334 Table[Binomial[4n, n-4], {n,4,30}] (* _Vincenzo Librandi_, Feb 01 2017 *)
%o A004334 (Magma) [Binomial(4*n, n-4): n in [4..30]]; // _Vincenzo Librandi_, Feb 01 2017
%o A004334 (PARI) a(n)=binomial(4*n,n-4) \\ _Charles R Greathouse IV_, Feb 01 2017
%o A004334 (Sage) [binomial(4*n,n-4) for n in (4..30)] # _G. C. Greubel_, Mar 21 2019
%o A004334 (GAP) List([4..30], n-> Binomial(4*n,n-4)); # _G. C. Greubel_, Mar 21 2019
%Y A004334 Cf. binomial(k*n, n-k): A000027 (k=1), A002694 (k=2), A004321 (k=3), this sequence (k=4), A004347 (k=5), A004361 (k=6), A004375 (k=7), A004389 (k=8), A281580 (k=9).
%K A004334 nonn,easy
%O A004334 4,2
%A A004334 _N. J. A. Sloane_