OFFSET
1,3
COMMENTS
B(n,p) = Sum_{i=0..n} p^i * Sum_{j=0..i} binomial(n,j)*B(j) where B(k) = k-th Bernoulli number. B(2n,p)/B(2n) takes integer values for all n if p=1,2,3,4,6. p=5 is the smallest integer for which B(2n,5)/B(2n) is not always integer-valued. And lim_{n->oo} B(2n,5)/(B(2n)*25^n) = (21-sqrt(5))/16.
FORMULA
Limit_{n->oo} B(2n, 7)/(B(2n)*49^n) = 1.0627516996902110782... is the smallest root of 1728*X^3 - 6192*X^2 + 7368*X - 2911 = 0.
MATHEMATICA
RealDigits[x/.FindRoot[ 1728x^3-6192x^2+7368x-2911==0, {x, 1}, WorkingPrecision-> 120]][[1]] (* Harvey P. Dale, Feb 19 2012 *)
PROG
(PARI) solve(q=1, 1.1, 1728*q^3-6192*q^2+7368*q-2911)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Benoit Cloitre, Jun 17 2004
STATUS
approved