A004343 Binomial coefficient C(5n,n-1).

1, 10, 105, 1140, 12650, 142506, 1623160, 18643560, 215553195, 2505433700, 29248649430, 342700125300, 4027810484880, 47465835030320, 560658857389200, 6635869816740560, 78682166288559225, 934433788613079150, 11113282527239083815, 132341572939212267400, 1577820333475709182860

Offset

1,2

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 = 1..922

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

From Peter Bala, Jul 21 2024: (Start)

a(n) = Sum_{k = 0..n-1} binomial(4*n+k, k).

a(n) = 5*(5*n - 1)*(5*n - 2)*(5*n - 3)*(5*n - 4)/((4*n - 4)*(4*n - 2)*(4*n - 1)*(4*n + 1)) * a(n-1) with a(1) = 1. (End)

a(n) ~ 5^(5*n+1/2) / (2^(8*n+7/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 08 2025

Mathematica

a[n_] := Binomial[5*n, n-1]; Array[a, 25] (* Amiram Eldar, Sep 08 2025 *)

Prog

(PARI) a(n) = binomial(5*n, n-1); \\ Amiram Eldar, Sep 08 2025

Crossrefs

Cf. A001791, A004319, A004331, A004356, A004369, A004382.

Sequence in context: A068618 A096484 A190955 * A163166 A068767 A233830

Adjacent sequences: A004340 A004341 A004342 * A004344 A004345 A004346

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved