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

1, 20, 276, 3276, 35960, 376992, 3838380, 38320568, 377348994, 3679075400, 35607051480, 342700125300, 3284214703056, 31368725759168, 298824321028320, 2840671544105280, 26958221130508525, 255485622301674660

Offset

4,2

References

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 4..1000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Daniel W. Stasiuk, An Enumeration Problem for Sequences of n-ary Trees Arising from Algebraic Operads, Master's Thesis, University of Saskatchewan-Saskatoon (2018).

Formula

From Ilya Gutkovskiy, Jan 31 2017: (Start)

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

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

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

Mathematica

Table[Binomial[4n, n-4], {n, 4, 30}] (* Vincenzo Librandi, Feb 01 2017 *)

Prog

(Magma) [Binomial(4*n, n-4): n in [4..30]]; // Vincenzo Librandi, Feb 01 2017
(PARI) a(n)=binomial(4*n, n-4) \\ Charles R Greathouse IV, Feb 01 2017
(SageMath) [binomial(4*n, n-4) for n in (4..30)] # G. C. Greubel, Mar 21 2019
(GAP) List([4..30], n-> Binomial(4*n, n-4)); # G. C. Greubel, Mar 21 2019

Crossrefs

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).

Sequence in context: A278722 A021264 A025928 * A019483 A018056 A021234

Adjacent sequences: A004331 A004332 A004333 * A004335 A004336 A004337

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved