A014609 a(n) = (5n)!/(5!^n).

1, 1, 252, 756756, 11732745024, 623360743125120, 88832646059788350720, 28837919555681211870935040, 18975581770994682860770223800320, 23183587808948692737291767860055162880, 49120458506088132224064306071170476903628800, 170878335353097656943918169452451079403744627916800

Offset

0,3

Comments

a(n) is also the constant term in product 1 <= i,j <= n, i different from j (1 - x_i/x_j)^5. - Sharon Sela (sharonsela(AT)hotmail.com), Feb 18 2002

References

George E. Andrews, Richard Askey, and Ranjan Roy, Special Functions, Cambridge University Press, 1998.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..105

Jean-Christophe Novelli and Jean-Yves Thibon, Hopf algebras of m-permutations, (m + 1)-ary trees, and m-parking functions, Advances in Applied Mathematics, Vol. 117 (2020), 102019; arXiv preprint, arXiv:1403.5962 [math.CO], 2014-2020.

Formula

a(n) ~ sqrt(Pi) * 5^(4*n+1/2) * n^(5*n+1/2) / (2^(3*n-1/2) * 3^n * exp(5*n)). - Amiram Eldar, Jun 09 2026

Mathematica

a[n_] := (5*n)!/(120^n); Array[a, 11, 0] (* Amiram Eldar, Jun 09 2026 *)

Prog

(PARI) a(n)=if(n<0, 0, (5*n)!/120^n)

Crossrefs

Column 5 of A187783.

Cf. A000680, A014606, A014608.

Sequence in context: A259452 A177302 A177303 * A172557 A068275 A068287

Adjacent sequences: A014606 A014607 A014608 * A014610 A014611 A014612

Keyword

nonn,easy

Author

BjornE (mdeans(AT)algonet.se)

Status

approved