The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A234854 E.g.f. satisfies: A'(x) = 1 + 4*A(x) + A(x)^2, where A(0)=0. 0
 1, 4, 18, 96, 624, 4896, 45072, 474624, 5619456, 73903104, 1069106688, 16872800256, 288483876864, 5311773904896, 104789944829952, 2205099306123264, 49302137885884416, 1167150882577711104, 29165495002777387008, 767163772371852066816, 21188300138891474632704 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA E.g.f.: Series_Reversion( Integral 1/(1 + 4*x + x^2) dx ). E.g.f.: (2-sqrt(3))*(exp(2*sqrt(3)*x)-1)/(1 + (4*sqrt(3) - 7)*exp(2*sqrt(3)*x)). - Vaclav Kotesovec, Jan 13 2014 a(n) ~ n! * ((2*sqrt(3))/log(7+4*sqrt(3)))^(n+1). - Vaclav Kotesovec, Jan 13 2014 O.g.f.: x/(1-4*x - 1*2*x^2/(1-8*x - 2*3*x^2/(1-12*x - 3*4*x^2/(1-16*x - 4*5*x^2/(1-20*x - 5*6*x^2/(1- .../(1-4*n*x - n*(n+1)*x^2/(1- ...))))))) (continued fraction). - Paul D. Hanna, Sep 01 2014 EXAMPLE E.g.f.: A(x) = x + 4*x^2/2! + 18*x^3/3! + 96*x^4/4! + 624*x^5/5! +... Related series. A(x)^2 = 2*x^2/2! + 24*x^3/3! + 240*x^4/4! + 2400*x^5/5! + 25488*x^6/6! +... MATHEMATICA Rest[FullSimplify[CoefficientList[Series[(2-Sqrt[3])*(E^(2*Sqrt[3]*x)-1)/(1 + (4*Sqrt[3]-7)*E^(2*Sqrt[3]*x)), {x, 0, 15}], x]*Range[0, 15]!]] (* Vaclav Kotesovec, Jan 13 2014 *) PROG (PARI) {a(n)=local(A=x); for(i=1, n, A=intformal(1+4*A+A^2 +x*O(x^n))); n!*polcoeff(A, n)} for(n=1, 25, print1(a(n), ", ")) (PARI) {a(n)=local(A=serreverse(intformal(1/(1+4*x+x^2 +x*O(x^n))))); n!*polcoeff(A, n)} for(n=1, 25, print1(a(n), ", ")) CROSSREFS Sequence in context: A001563 A094304 A094258 * A334735 A086681 A054139 Adjacent sequences:  A234851 A234852 A234853 * A234855 A234856 A234857 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 09 2014 STATUS approved

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

Last modified July 5 05:47 EDT 2022. Contains 355087 sequences. (Running on oeis4.)