OFFSET
1,3
REFERENCES
J. Spanier and K. B. Oldham, An Atlas of Functions, Hemisphere, NY, 1987, p. 35, Eq. 4:2:1.
LINKS
FORMULA
a(n) ~ 16 * 2^(n+1/2) * Pi^(1/2-2*n) * n^(3/2) * (n/e)^(3*n). - Vladimir Reshetnikov, Sep 05 2016
From Peter Luschny, May 17 2018: (Start)
a(n) ~ 8*sqrt(2*n*Pi)*(2*Pi)^n*(n/(Pi*e))^(3*n)*(2*n+1).
a(n) = |(2^(n+2)*Pochhammer(1/2, n+1)*Bernoulli(2*n)|. (End)
a(n) = -(-2)^(n+3)*n*Zeta(1-2*n)*(n+1/2)!/sqrt(Pi). - Peter Luschny, Jun 21 2020
MAPLE
a:= n-> -(-1)^n*2*(2*n+1)!*bernoulli(2*n)/(n!*2^n):
seq(a(n), n=1..20); # Alois P. Heinz, Jun 13 2016
MATHEMATICA
Table[-((-1)^n 2(2n+1)!BernoulliB[2n])/(n! 2^n), {n, 20}] (* Harvey P. Dale, Oct 05 2012 *)
Table[2 (2n+1)!! Abs@BernoulliB[2n], {n, 20}] (* Vladimir Reshetnikov, Jun 05 2016 *)
PROG
(PARI) a(n)=if(n<1, 0, -(-1)^n*2*(2*n+1)!*bernfrac(2*n)/(n!*2^n))
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
David W. Cantrell (DWCantrell(AT)sigmaxi.net)
STATUS
approved