A211393 E.g.f.: exp( Sum_{n>=1} x^(2*n) / (2*n*(2*n-1)) ) = Sum_{n>=0} a(n)*x^(2*n)/(2*n)!.

1, 1, 5, 69, 2057, 111465, 9704397, 1244894637, 221232748305, 52050205317969, 15662965291361685, 5867751811494701205, 2677887724787888962329, 1462537391313912349354425, 941812152929331549233701725, 706153411932893616967191153405

Offset

0,3

Comments

Sum_{n>=0} a(n)/(2*n)! = 2.

Links

Table of n, a(n) for n=0..15.

Formula

E.g.f.: sqrt(1-x^2)*exp(x*atanh(x)). - Vladimir Kruchinin, Feb 26 2015

Example

E.g.f.: A(x) = 1 + x^2/2! + 5*x^4/4! + 69*x^6/6! + 2057*x^8/8! +... where log(A(x)) = x^2/(1*2) + x^4/(3*4) + x^6/(5*6) + x^8/(7*8) +...

Prog

(PARI) {a(n)=(2*n)!*polcoeff(exp(sum(m=1, n, x^(2*m)/(2*m*(2*m-1)))+x*O(x^(2*n))), 2*n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Sequence in context: A231294 A302543 A157038 * A231355 A145632 A299318

Adjacent sequences: A211390 A211391 A211392 * A211394 A211395 A211396

Keyword

nonn

Author

Paul D. Hanna, Feb 08 2013

Status

approved