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A268432 a(n) = Pochhammer(n+1, n)/Clausen(n, 1) = A001813(n) / A160014(n, 1). 2
1, 1, 2, 60, 56, 15120, 15840, 8648640, 17297280, 8821612800, 10158220800, 14079294028800, 474467051520, 32382376266240000, 582882772792320000, 101421602465863680000, 24659370011308032000, 415017197290314178560000, 72810034612335820800000, 2149789081963827444940800000 (list; graph; refs; listen; history; text; internal format)
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

(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)]

CROSSREFS

Cf. A001813, A027642, A160014, A264437.

Sequence in context: A262638 A202622 A113549 * A117482 A078511 A087004

Adjacent sequences:  A268429 A268430 A268431 * A268433 A268434 A268435

KEYWORD

nonn

AUTHOR

Peter Luschny, Feb 14 2016

STATUS

approved

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Last modified October 15 07:56 EDT 2019. Contains 328026 sequences. (Running on oeis4.)