login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143137 E.g.f. satisfies A(x) = sinh(x + A(x)^2). 4
1, 2, 13, 140, 2101, 40502, 954073, 26557400, 852911401, 31042592042, 1262704455013, 56767589130980, 2795116027239901, 149590982933830622, 8646295934108179633, 536766403519254357680, 35620604244949591333201 (list; graph; refs; listen; history; text; internal format)
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

Cf. A143135, A143136.

Sequence in context: A152059 A132063 A318003 * A003414 A003326 A207493

Adjacent sequences:  A143134 A143135 A143136 * A143138 A143139 A143140

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 27 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 16 03:14 EST 2019. Contains 330013 sequences. (Running on oeis4.)