A004340 Binomial coefficient C(4n,n-10).

1, 44, 1128, 22100, 367290, 5461512, 74974368, 969443904, 11969016345, 142466675900, 1646492110120, 18574174153080, 205371886988268, 2232785266876080, 23929614612052080, 253338471349988640, 2653828761561014310, 27545633466126922440, 283623240203200959600

Offset

10,2

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 = 10..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+10)*(n+3)*(n-10)*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+21/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 07 2025

Mathematica

a[n_] := Binomial[4*n, n-10]; Array[a, 20, 10] (* Amiram Eldar, Sep 07 2025 *)

Crossrefs

Sequence in context: A345410 A114170 A130645 * A387015 A394272 A387743

Adjacent sequences: A004337 A004338 A004339 * A004341 A004342 A004343

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved