A004339 Binomial coefficient C(4n,n-9).

1, 40, 946, 17296, 270725, 3819816, 50063860, 621216192, 7392009768, 85113005120, 954526728530, 10477677064400, 112992892764570, 1200635647008336, 12599288291657880, 130815226545884704, 1345860629046814650, 13737466530433485840, 139258480300974996780, 1403188662057941589600

Offset

9,2

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 = 9..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*(3*n+8)*(3*n+7)*(n+3)*(n-9)*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+19/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 07 2025

Mathematica

a[n_] := Binomial[4*n, n-9]; Array[a, 20, 9] (* Amiram Eldar, Sep 07 2025 *)

Crossrefs

Sequence in context: A140220 A130610 A279582 * A172510 A004349 A016092

Adjacent sequences: A004336 A004337 A004338 * A004340 A004341 A004342

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved