A004333 Binomial coefficient C(4n,n-3).

1, 16, 190, 2024, 20475, 201376, 1947792, 18643560, 177232627, 1677106640, 15820024220, 148902215280, 1399358844975, 13136858812224, 123234279768160, 1155454041309504, 10830060261901380, 101489773667796800, 950974260789566790, 8910491434304783400, 83491932238832602485

Offset

3,2

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

Seiichi Manyama, Table of n, a(n) for n = 3..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].

Formula

D-finite with recurrence -3*(n-3)*(3*n+2)*(3*n+1)*(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

a(n) ~ 2^(8*n+1/2) / (3^(3*n+7/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 07 2025

Maple

A004333:=n->binomial(4*n, n-3); seq(A004333(n), n=3..100); # Wesley Ivan Hurt, Mar 15 2014

Mathematica

Table[Binomial[4 n, n - 3], {n, 3, 100}] (* Wesley Ivan Hurt, Mar 15 2014 *)

Crossrefs

Sequence in context: A231834 A181277 A181269 * A383205 A016237 A036735

Adjacent sequences: A004330 A004331 A004332 * A004334 A004335 A004336

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved