A222055 E.g.f.: exp( Sum_{n>=1} x^(2*n-1) / (n*(2*n-1)) ).

1, 1, 1, 2, 5, 19, 79, 454, 2673, 20789, 159101, 1568786, 14804701, 177333727, 1991552627, 28122135014, 366398602529, 5965436400009, 88463085201433, 1632635041751362, 27151272591960661, 560416797991873451, 10329130452139887191, 235856196146890193062

Offset

0,4

Comments

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

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

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

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

Example

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

Mathematica

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

Prog

(PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n, x^(2*m-1)/(m*(2*m-1)))+x*O(x^(2*n))), n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=n!*polcoeff( (1+x)^2 / (1-x^2 +x^2*O(x^n))^(1-1/x), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A150027 A277969 A058131 * A228569 A204328 A288911

Adjacent sequences: A222052 A222053 A222054 * A222056 A222057 A222058

Keyword

nonn

Author

Paul D. Hanna, Feb 14 2013

Status

approved