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

Author

Benoit Cloitre, Jun 17 2004

Keywords

• cons
• nonn

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.

Crossrefs

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

Programs

Mathematica

RealDigits[x/.FindRoot[ 1728x^3-6192x^2+7368x-2911==0,{x,1}, WorkingPrecision-> 120]][[1]] (* Harvey P. Dale, Feb 19 2012 *)

PARI

solve(q=1,1.1,1728*q^3-6192*q^2+7368*q-2911)

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.