A004346 Binomial coefficient C(5n,n-4).

1, 25, 435, 6545, 91390, 1221759, 15890700, 202927725, 2558620845, 31966749880, 396704524216, 4898229264825, 60246643120300, 738799683460650, 9038619861406740, 110375347398090219, 1345860629046814650, 16391295291994500150, 199439701243274033850, 2424792109500392414475

Offset

4,2

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

Table of n, a(n) for n=4..23.

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 -8*(4*n+3)*(n-4)*(2*n+1)*(4*n+1)*(n+1)*a(n) + 5*n*(5*n-4)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1) = 0. - R. J. Mathar, Mar 19 2025

a(n) ~ 5^(5*n+1/2) / (2^(8*n+19/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 08 2025

Mathematica

a[n_] := Binomial[5*n, n-4]; Array[a, 25, 4] (* Amiram Eldar, Sep 08 2025 *)

Prog

(PARI) a(n) = binomial(5*n, n-4); \\ Amiram Eldar, Sep 08 2025

Crossrefs

Sequence in context: A019722 A180800 A387367 * A021324 A092430 A018207

Adjacent sequences: A004343 A004344 A004345 * A004347 A004348 A004349

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved