A222055 - OEIS

%I #11 Jun 04 2013 03:36:20

%S 1,1,1,2,5,19,79,454,2673,20789,159101,1568786,14804701,177333727,

%T 1991552627,28122135014,366398602529,5965436400009,88463085201433,

%U 1632635041751362,27151272591960661,560416797991873451,10329130452139887191,235856196146890193062

%N E.g.f.: exp( Sum_{n>=1} x^(2*n-1) / (n*(2*n-1)) ).

%C Sum_{n>=0} a(n)/n! = 4.

%C The radius of convergence of the e.g.f. is |x| <= 1.

%H Vincenzo Librandi, <a href="/A222055/b222055.txt">Table of n, a(n) for n = 0..200</a>

%F E.g.f.: (1+x)^2 / (1-x^2)^(1-1/x).

%F a(n) ~ 15*(n-2)!/4 if n is even and a(n) ~ 17*(n-2)!/4 if n is odd. - _Vaclav Kotesovec_, Jun 02 2013

%e E.g.f.: A(x) = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 19*x^5/5! + 79*x^6/6! + 454*x^7/7! + 2673*x^8/8! + 20789*x^9/9! +...

%e where

%e log(A(x)) = x/(1*1) + x^3/(2*3) + x^5/(3*5) + x^7/(4*7) + x^9/(5*9) +...

%t CoefficientList[Series[(1+x)^2/(1-x^2)^(1-1/x), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 02 2013 *)

%o (PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n, x^(2*m-1)/(m*(2*m-1)))+x*O(x^(2*n))), n)}

%o for(n=0, 30, print1(a(n), ", "))

%o (PARI) {a(n)=n!*polcoeff( (1+x)^2 / (1-x^2 +x^2*O(x^n))^(1-1/x),n)}

%o for(n=0, 30, print1(a(n), ", "))

%K nonn

%O 0,4

%A _Paul D. Hanna_, Feb 14 2013