A134354 Integer nearest to expression 2*Pi*n^(2*n + 1)*e^(-2*n).

1, 4, 34, 553, 13929, 504211, 24804343, 1592201163, 129266762933, 12950610156346, 1569397748147942, 226278584786787356, 38281932323382964780, 7510129222684066040577, 1691120063240224327004643, 433227358889999321792523782, 125279419365525918256280791436

Offset

1,2

Comments

Integers in this sequence are <= (n!)^2 (see A001044).

Links

Table of n, a(n) for n=1..17.

Formula

a(n) = round(2*Pi*n^(2*n + 1)*e^(-2*n)).

Mathematica

Table[Round[2 Pi n^(2 n + 1)E^(-2 n)], {n, 1, 30}]

Prog

(Python)
import mpmath
from mpmath import iv
def a(n):
    dps = 50
    while True:
        iv.dps = mpmath.mp.dps = dps
        v = 2 * iv.pi * (iv.mpf(n) ** (2 * n + 1)) * iv.exp(-2 * n)
        lo_raw, hi_raw = v._mpi_
        lo_round = int(mpmath.floor(mpmath.mpf(lo_raw) + 0.5))
        hi_round = int(mpmath.floor(mpmath.mpf(hi_raw) + 0.5))
        if lo_round == hi_round:
            return lo_round
dps *= 2  # Falk Hüffner, May 25 2026

Crossrefs

Cf. A001044, A134354.

Sequence in context: A222077 A081972 A158961 * A333981 A030243 A222789

Adjacent sequences: A134351 A134352 A134353 * A134355 A134356 A134357

Keyword

nonn

Author

Artur Jasinski, Oct 22 2007

Extensions

a(12)-a(15) corrected and a(16)-a(17) added by Falk Hüffner, May 25 2026

Status

approved