login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A227466
E.g.f. equals the series reversion of tanh(x) / exp(x).
2
1, 2, 11, 96, 1149, 17520, 324855, 7096320, 178495065, 5081045760, 161485639875, 5668185600000, 217773547039125, 9090267234048000, 409648199646660975, 19822083757572096000, 1025047834112461784625, 56415976360602034176000, 3292602426688307236378875
OFFSET
1,2
COMMENTS
Note that arctanh(x) = log((1+x)/(1-x))/2.
FORMULA
E.g.f. A(x) satisfies: A(x) = arctanh(x*exp(A(x))).
a(n) ~ ((1+sqrt(5))/2)^(5*n/2) * n^(n-1) / (5^(1/4) * exp(n)). - Vaclav Kotesovec, Jan 10 2014
EXAMPLE
E.g.f.: A(x) = x + 2*x^2/2! + 11*x^3/3! + 96*x^4/4! + 1149*x^5/5! + 17520*x^6/6! + ...
where A( tanh(x)/exp(x) ) = x.
MATHEMATICA
Rest[CoefficientList[InverseSeries[Series[Tanh[x]/E^x, {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 10 2014 *)
PROG
(PARI) {a(n)=local(X=x+x*O(x^n)); n!*polcoeff(serreverse(tanh(X)/exp(X)), n)}
for(n=1, 25, print1(a(n), ", "))
(PARI) {a(n)=local(A=x); for(i=1, n, A=atanh(x*exp(A+x*O(x^n)))); n!*polcoeff(A, n)}
for(n=1, 25, print1(a(n), ", "))
CROSSREFS
Cf. A227465.
Sequence in context: A138210 A227465 A295099 * A136344 A055680 A260957
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 14 2013
STATUS
approved