A203229 (n-1)-st elementary symmetric function of (1,16,...,n^4).

1, 17, 1393, 357904, 224021776, 290539581696, 697854274212096, 2859056348455305216, 18760911610508623282176, 187626456226399005573120000, 2747212346823835568109649920000, 56968733990900457398848318341120000, 1627136655389966817590114762694328320000

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Formula

a(n) ~ 2 * Pi^6 * n^(4*n+2) / (45*exp(4*n)). - Vaclav Kotesovec, Aug 27 2017

Sum_{n>=1} a(n) * x^n / (n!)^4 = polylog(4,x) / (1 - x). - Ilya Gutkovskiy, Jul 14 2020

Mathematica

f[k_] := k^4; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 14}]
(* Alternative: *)
Table[(n!)^4 * Sum[1/i^4, {i, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Aug 27 2017 *)

Prog

(Python)
from math import factorial
from sympy import harmonic
def A203229(n): return int(factorial(n)**4*harmonic(n, 4)) # Chai Wah Wu, May 08 2026

Crossrefs

Cf. A000583, A203148.

Column k=4 of A291556.

Sequence in context: A219562 A183236 A007410 * A269791 A256020 A072160

Adjacent sequences: A203226 A203227 A203228 * A203230 A203231 A203232

Keyword

nonn,easy

Author

Clark Kimberling, Dec 30 2011

Extensions

a(13) from Chai Wah Wu, May 09 2026

Status

approved