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A354862 a(n) = n! * Sum_{d|n} (n/d)! / d!. 2
1, 5, 37, 601, 14401, 520801, 25401601, 1626189601, 131682257281, 13168407228481, 1593350922240001, 229442707280223361, 38775788043632640001, 7600054676241325858561, 1710012252750418295078401, 437763137119219420513804801, 126513546505547170185216000001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

E.g.f.: Sum_{k>0} k! * (exp(x^k) - 1).

If p is prime, a(p) = 1 + (p!)^2 = A020549(p).

PROG

(PARI) a(n) = n!*sumdiv(n, d, (n/d)!/d!);

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k!*(exp(x^k)-1))))

(Python)

from math import factorial

from sympy import divisors

def A354862(n):

    f = factorial(n)

    return sum(f*(a := factorial(n//d))//(b:= factorial(d)) + (f*b//a if d**2 < n else 0) for d in divisors(n, generator=True) if d**2 <= n) # Chai Wah Wu, Jun 09 2022

CROSSREFS

Cf. A020549, A057625, A121860, A354843, A354863.

Sequence in context: A244820 A246534 A095957 * A121834 A215233 A083846

Adjacent sequences:  A354859 A354860 A354861 * A354863 A354864 A354866

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 09 2022

STATUS

approved

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Last modified September 28 14:44 EDT 2022. Contains 357073 sequences. (Running on oeis4.)