A096050 Decimal expansion of lim_{n->oo} B(2n,7)/(B(2n)*49^n) (see comment for B(n,k) definition).

1, 0, 6, 2, 7, 5, 1, 6, 9, 9, 6, 9, 0, 2, 1, 1, 0, 7, 8, 2, 4, 5, 8, 3, 2, 5, 1, 9, 3, 3, 2, 6, 2, 6, 6, 9, 8, 2, 2, 7, 9, 5, 4, 2, 1, 1, 5, 1, 7, 2, 6, 6, 3, 1, 5, 7, 7, 2, 4, 0, 8, 4, 2, 6, 8, 1, 7, 1, 9, 1, 0, 5, 7, 9, 2, 3, 9, 1, 8, 7, 8, 5, 9, 0, 4, 0, 0, 9, 5, 8, 2, 1, 1, 2, 2, 3, 5, 7, 7, 1, 3, 8, 8, 8, 2

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.

Links

Table of n, a(n) for n=1..105.

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

Cf. A096045, A096046, A096047, A096048, A096049.

Sequence in context: A340421 A244922 A153313 * A115731 A163340 A326823

Adjacent sequences: A096047 A096048 A096049 * A096051 A096052 A096053

Keyword

cons,nonn

Author

Benoit Cloitre, Jun 17 2004

Status

approved