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

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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].

Programs

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 *)

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