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

%I #33 Feb 06 2024 01:38:42

%S 1,20,276,3276,35960,376992,3838380,38320568,377348994,3679075400,

%T 35607051480,342700125300,3284214703056,31368725759168,

%U 298824321028320,2840671544105280,26958221130508525,255485622301674660

%N Binomial coefficient C(4n,n-4).

%D 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 Vincenzo Librandi, <a href="/A004334/b004334.txt">Table of n, a(n) for n = 4..1000</a>

%H 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 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 From _Ilya Gutkovskiy_, Jan 31 2017: (Start)

%F E.g.f.: (1/24)*x^4*3F3(17/4,9/2,19/4; 17/3,6,19/3; 256*x/27).

%F a(n) ~ 2^(8*n+1/2)/(sqrt(Pi*n)*3^(3*n+9/2)). (End)

%t Table[Binomial[4n, n-4], {n,4,30}] (* _Vincenzo Librandi_, Feb 01 2017 *)

%o (Magma) [Binomial(4*n, n-4): n in [4..30]]; // _Vincenzo Librandi_, Feb 01 2017

%o (PARI) a(n)=binomial(4*n,n-4) \\ _Charles R Greathouse IV_, Feb 01 2017

%o (Sage) [binomial(4*n,n-4) for n in (4..30)] # _G. C. Greubel_, Mar 21 2019

%o (GAP) List([4..30], n-> Binomial(4*n,n-4)) # _G. C. Greubel_, Mar 21 2019

%Y 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 nonn,easy

%O 4,2

%A _N. J. A. Sloane_