0,2

n-th elementary symmetric function of the first n+1 odd positive integers.

a(n) = (2*n+1)!! * sum[ k=0..n ] 1/(2*k+1).

a(n) is coefficient of x^(2*n+2) in (arctanh x)^2, multiplied by (n+1)*(2*n+1)!!.

sum[(-1)^(k+1-i) 2^(n-1) binomial(i-1, k) s1(n, i), i=k+1..n] with k = 1, where s1(n, i) are unsigned Stirling numbers of the first kind - Victor Adamchik (adamchik(AT)ux10.sp.cs.cmu.edu), Jan 23, 2001

a(n) ~ 2^(1/2)*log(n)*n*2^n*e^-n*n^n - Joe Keane (jgk(AT)jgk.org), Jun 06 2002

E.g.f.: 1/2*(1-2*x)^(-3/2)*(2-ln(1-2*x)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 19 2003

Sum(n>=1; a(n-1)/(n!*n*2^n)) = (Pi/2)^2. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Aug 12 2003

(arctanh x)^2 = x^2 + 2/3*x^4 + 23/45*x^6 + 44/105*x^8 + ...

Cf. A000254, A024199, A049034.

Cf. A002428.

Sequence in context: A083355 A025550 A067545 this_sequence A089465 A106174 A056814

Adjacent sequences: A004038 A004039 A004040 this_sequence A004042 A004043 A004044

nonn

Joe Keane (jgk(AT)jgk.org)