OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..150
FORMULA
E.g.f.: A(x) = sinh(G(x)) where G(x) = Series_Reversion( x - sinh(x)^2 ) is the e.g.f. of A143136.
a(n) ~ sqrt(1+sqrt(2)) * 2^(n-7/4) * n^(n-1) / (exp(n) * (1-sqrt(2)+log(1+sqrt(2)))^(n-1/2)). - Vaclav Kotesovec, Jan 08 2014
EXAMPLE
A(x) = x + 2*x^2/2! + 13*x^3/3! + 140*x^4/4! + 2101*x^5/5! +...
A(x) = sinh(G(x)) where G(x) is the e.g.f. of A143136:
G(x) = x + 2*x^2/2! + 12*x^3/3! + 128*x^4/4! + 1920*x^5/5! +...
MATHEMATICA
Rest[CoefficientList[InverseSeries[Series[-x^2 + ArcSinh[x], {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 08 2014 *)
PROG
(PARI) {a(n)=n!*polcoeff(sinh(serreverse(x-sinh(x+x*O(x^n))^2)), n)}
(PARI) {a(n)=local(A=x); for(i=0, n, A=x + sinh(A)^2); n!*polcoeff(sinh(A), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 27 2008
STATUS
approved