A004356 Binomial coefficient C(6n,n-1).

1, 12, 153, 2024, 27405, 376992, 5245786, 73629072, 1040465790, 14783142660, 210980549208, 3022285436352, 43430966148115, 625806790696080, 9038619861406740, 130815226545884704, 1896724514424115530, 27545633466126922440, 400617826787021355435, 5834104414094383310520

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..853

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 5*(n-1)*(5*n+1)*(5*n-3)*(5*n-2)*(5*n-1)*a(n) - 72*(6*n-5)*(6*n-1)*(3*n-1)*(2*n-1)*(3*n-2)*a(n-1) = 0. - R. J. Mathar, Mar 19 2025

a(n) ~ 64^n * 3^(6*n+1/2) / (5^(5*n+3/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 09 2025

a(n) = A004357(n)*(5*n+2)/(n-1). - R. J. Mathar, Mar 14 2026

Mathematica

Table[Binomial[6n, n-1], {n, 20}] (* Harvey P. Dale, Mar 04 2017 *)

Prog

(PARI) a(n) = binomial(6*n, n-1); \\ Amiram Eldar, Sep 09 2025

Crossrefs

Cf. A001791, A004319, A004331, A004343, A004369, A004382.

Sequence in context: A121195 A189490 A180808 * A036360 A120657 A015612

Adjacent sequences: A004353 A004354 A004355 * A004357 A004358 A004359

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved