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

Offset: 0

Author

Peter Luschny, Feb 14 2016

Keywords

• nonn

Crossrefs

Cf. A001813, A027642, A160014, A264437.

Programs

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);

Sage

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)]

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.