Voozh

A268432

a(n) = Pochhammer(n+1, n)/Clausen(n, 1) = A001813(n) / A160014(n, 1).

1, 1, 2, 60, 56, 15120, 15840, 8648640, 17297280, 8821612800, 10158220800, 14079294028800, 474467051520, 32382376266240000, 582882772792320000, 101421602465863680000, 24659370011308032000, 415017197290314178560000, 72810034612335820800000, 2149789081963827444940800000

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

FORMULA

Let b(n) = Pochhammer(n+1,n)/denominator(Bernoulli(n)) then a(2*n) = b(2*n) for n >= 0 and 2*a(2*n+1) = b(2*n+1) for n >= 1 by the von Staudt-Clausen theorem.

MAPLE

a := proc(n) numtheory[divisors](n); map(i->i+1, %);

iquo(mul(4*k+2, k in (0..n-1)), mul(k, k in select(isprime, %))) end:

seq(a(n), n=0..19);

PROG

(SageMath)

def A268432(n):

if n <= 1: return 1

r = rising_factorial(n+1, n)//bernoulli(n).denominator()

return r if is_even(n) else r//2

[A268432(n) for n in range(20)]

CROSSREFS